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What do you mean by the square root of integers\u00a0<\/strong><\/h2>\nAn integer is a number that doesn’t have a decimal or fractional part. Integers range from negative to positive numbers, including zero.<\/span><\/p>\n <\/p>\n
Types of integers –<\/span><\/h3>\nThe following are the types on integers-<\/span><\/p>\nPositive Integers<\/strong>: An integer is said to be positive if it is greater than zero. Example: 1, 2, 3 and so on.<\/span><\/p>\nNegative Integers:<\/strong> An integer is said to be negative if it is less than zero. For example, -1, -2 and so on.<\/span><\/p>\nIs zero an integer?<\/strong><\/p>\nZero is neither a negative integer nor a positive one. Instead, it is a whole number.<\/span><\/p>\nFinding out square roots of positive integers –<\/strong><\/h3>\nDetermining the square root of a positive integer is a piece of cake. There is little to no hassle in finding out these square roots. It is the same as taking a square root of any number.<\/span><\/p>\nHowever, square roots of integers either have a positive or a negative sign.<\/span><\/p>\n\u221a16 can be written as 4 and as -4 as the minus sign gets turned into a positive sign after the number is squared.<\/span><\/p>\nFinding out square roots of negative integers –<\/strong><\/h3>\nCalculating the square root of a positive integer is relatively easier than that of a negative integer. It is, in fact, not practically possible to solve the square root of a negative integer.<\/span><\/p>\nThis happens because a square root of a number is the value that gives the number when multiplied by itself. This is simply not possible in the case of negative numbers, as when two negative digits are multiplied, the result is always bound to be positive. When multiplied with itself, no number can ever yield a negative number, thereby making it complicated to solve the square root of a negative integer.<\/span><\/p>\nFinding out square roots of integers with an odd number of digits –<\/strong><\/h3>\nTo calculate the square roots of a given integer with an odd number of digits, we follow these steps:-<\/span><\/p>\nAssumption – the given three digit integer is 289<\/span><\/p>\n Step 1:<\/strong><\/p>\nWrite 289 in pairs of digits.\u00a0 Pair the digits beginning from the right. For example, 89 will be the first pair, and 2 will be left as a single digit.<\/span><\/p>\nStep 2:<\/strong><\/p>\nWe’ll find the integer part (i.e., the divisor) of the square root of the single digit on the left. In this case, the square root of 1 will give us 1. Here, we will consider 1 because its square root is less than 2. This will be the digit of the importance of the resultant square root. Write it at the top as the quotient. This is the current digit.<\/span><\/p>\nStep 3:<\/strong><\/p>\nNow, we write the square of the current digit below the digit of significance and find the difference between the two (which is 1 here)\u2014bringing down the next pair of digits on the right, i.e., 89, to append to the difference 1. The resultant number is then 189. We’ll call this the new number. This will complete our first stage of finding the digit of the significance of the square root.<\/span><\/p>\nStep 4:<\/strong><\/p>\nOn the left of the new number, we’ll write the double of the square root result formed till this stage. At this point, it will be just 2 (as 1\u00d72=2). Next, we need to find a digit to append to 2 so that the product of the two-digit number formed and the digit appended is just less than or equal to the new number 189.<\/span><\/p>\nAppending 7 to 2 will form 27, and 7×27 gives us 189 with a remainder of 0. 7 now becomes the current digit, and it is appended to the square root result at the top to form 17 as the final square root.<\/span><\/p>\nThis method stops when the remainder is 0.<\/span><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Sq-root-of-Integers-01.png\")
<\/span><\/p>\n<\/span><\/p>\nFinding out the square root of integers with even number of digits –<\/strong><\/h3>\nTo calculate the square roots of a given integer with an even number of digits, we follow these steps:-<\/span><\/p>\nAssumption – the given integer is 7921.<\/span><\/p>\nStep 1:<\/strong><\/p>\nWe begin by writing 7921 in pairs of digits from the right. The pairs thus formed are ’79’ ’21’.<\/span><\/p>\nStep 2:<\/strong><\/p>\nNow the integer part (i.e., the divisor) of the square root of 79 is 8, and its square gives us 64. Here, we are considering 8 because its square root is less than 79. Subtracting 64 from 79 gives us 15 as a remainder. This number then becomes 15 21 when the next pair of digits is brought down. Thus, 8 is the current divisor and forms the digit of the significance of the square root result.<\/span><\/p>\nStep 3:<\/strong><\/p>\nSquare root result formed till now 8X2= 16. Now, by appending 9 to 16. We are considering 9 after a method of trials and errors. We get the new number as 169, so that 9\u00d7169=1521. 9 is appended to 8, and the square root result thus formed is 89. As the remainder becomes zero, the process ends, and 89 is our desired answer.<\/span><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Sq-root-of-Integers-02.png\")
<\/span><\/p>\n[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics
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\nGeometry<\/a><\/div>\nTrigonometry<\/a><\/div>\nOperations<\/a><\/div>\nNumbers<\/a><\/div>\n<\/div>\n[\/et_pb_text][et_pb_text admin_label=”Related Concepts
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\nSquare and Square roots<\/a><\/div>\nValue of root 2<\/a><\/div>\n
<\/p>\n
Types of integers –<\/span><\/h3>\nThe following are the types on integers-<\/span><\/p>\nPositive Integers<\/strong>: An integer is said to be positive if it is greater than zero. Example: 1, 2, 3 and so on.<\/span><\/p>\nNegative Integers:<\/strong> An integer is said to be negative if it is less than zero. For example, -1, -2 and so on.<\/span><\/p>\nIs zero an integer?<\/strong><\/p>\nZero is neither a negative integer nor a positive one. Instead, it is a whole number.<\/span><\/p>\nFinding out square roots of positive integers –<\/strong><\/h3>\nDetermining the square root of a positive integer is a piece of cake. There is little to no hassle in finding out these square roots. It is the same as taking a square root of any number.<\/span><\/p>\nHowever, square roots of integers either have a positive or a negative sign.<\/span><\/p>\n\u221a16 can be written as 4 and as -4 as the minus sign gets turned into a positive sign after the number is squared.<\/span><\/p>\nFinding out square roots of negative integers –<\/strong><\/h3>\nCalculating the square root of a positive integer is relatively easier than that of a negative integer. It is, in fact, not practically possible to solve the square root of a negative integer.<\/span><\/p>\nThis happens because a square root of a number is the value that gives the number when multiplied by itself. This is simply not possible in the case of negative numbers, as when two negative digits are multiplied, the result is always bound to be positive. When multiplied with itself, no number can ever yield a negative number, thereby making it complicated to solve the square root of a negative integer.<\/span><\/p>\nFinding out square roots of integers with an odd number of digits –<\/strong><\/h3>\nTo calculate the square roots of a given integer with an odd number of digits, we follow these steps:-<\/span><\/p>\nAssumption – the given three digit integer is 289<\/span><\/p>\n Step 1:<\/strong><\/p>\nWrite 289 in pairs of digits.\u00a0 Pair the digits beginning from the right. For example, 89 will be the first pair, and 2 will be left as a single digit.<\/span><\/p>\nStep 2:<\/strong><\/p>\nWe’ll find the integer part (i.e., the divisor) of the square root of the single digit on the left. In this case, the square root of 1 will give us 1. Here, we will consider 1 because its square root is less than 2. This will be the digit of the importance of the resultant square root. Write it at the top as the quotient. This is the current digit.<\/span><\/p>\nStep 3:<\/strong><\/p>\nNow, we write the square of the current digit below the digit of significance and find the difference between the two (which is 1 here)\u2014bringing down the next pair of digits on the right, i.e., 89, to append to the difference 1. The resultant number is then 189. We’ll call this the new number. This will complete our first stage of finding the digit of the significance of the square root.<\/span><\/p>\nStep 4:<\/strong><\/p>\nOn the left of the new number, we’ll write the double of the square root result formed till this stage. At this point, it will be just 2 (as 1\u00d72=2). Next, we need to find a digit to append to 2 so that the product of the two-digit number formed and the digit appended is just less than or equal to the new number 189.<\/span><\/p>\nAppending 7 to 2 will form 27, and 7×27 gives us 189 with a remainder of 0. 7 now becomes the current digit, and it is appended to the square root result at the top to form 17 as the final square root.<\/span><\/p>\nThis method stops when the remainder is 0.<\/span><\/p>\n<\/span><\/p>\n<\/span><\/p>\nFinding out the square root of integers with even number of digits –<\/strong><\/h3>\nTo calculate the square roots of a given integer with an even number of digits, we follow these steps:-<\/span><\/p>\nAssumption – the given integer is 7921.<\/span><\/p>\nStep 1:<\/strong><\/p>\nWe begin by writing 7921 in pairs of digits from the right. The pairs thus formed are ’79’ ’21’.<\/span><\/p>\nStep 2:<\/strong><\/p>\nNow the integer part (i.e., the divisor) of the square root of 79 is 8, and its square gives us 64. Here, we are considering 8 because its square root is less than 79. Subtracting 64 from 79 gives us 15 as a remainder. This number then becomes 15 21 when the next pair of digits is brought down. Thus, 8 is the current divisor and forms the digit of the significance of the square root result.<\/span><\/p>\nStep 3:<\/strong><\/p>\nSquare root result formed till now 8X2= 16. Now, by appending 9 to 16. We are considering 9 after a method of trials and errors. We get the new number as 169, so that 9\u00d7169=1521. 9 is appended to 8, and the square root result thus formed is 89. As the remainder becomes zero, the process ends, and 89 is our desired answer.<\/span><\/p>\n<\/span><\/p>\n[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics
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\nGeometry<\/a><\/div>\nTrigonometry<\/a><\/div>\nOperations<\/a><\/div>\nNumbers<\/a><\/div>\n<\/div>\n[\/et_pb_text][et_pb_text admin_label=”Related Concepts
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[\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” hover_enabled=”0″ locked=”off” global_colors_info=”{}” sticky_enabled=”0″]<\/p>\n
\nSquare and Square roots<\/a><\/div>\nValue of root 2<\/a><\/div>\n
Positive Integers<\/strong>: An integer is said to be positive if it is greater than zero. Example: 1, 2, 3 and so on.<\/span><\/p>\n Negative Integers:<\/strong> An integer is said to be negative if it is less than zero. For example, -1, -2 and so on.<\/span><\/p>\n Is zero an integer?<\/strong><\/p>\n Zero is neither a negative integer nor a positive one. Instead, it is a whole number.<\/span><\/p>\n Determining the square root of a positive integer is a piece of cake. There is little to no hassle in finding out these square roots. It is the same as taking a square root of any number.<\/span><\/p>\n However, square roots of integers either have a positive or a negative sign.<\/span><\/p>\n \u221a16 can be written as 4 and as -4 as the minus sign gets turned into a positive sign after the number is squared.<\/span><\/p>\n Calculating the square root of a positive integer is relatively easier than that of a negative integer. It is, in fact, not practically possible to solve the square root of a negative integer.<\/span><\/p>\n This happens because a square root of a number is the value that gives the number when multiplied by itself. This is simply not possible in the case of negative numbers, as when two negative digits are multiplied, the result is always bound to be positive. When multiplied with itself, no number can ever yield a negative number, thereby making it complicated to solve the square root of a negative integer.<\/span><\/p>\n To calculate the square roots of a given integer with an odd number of digits, we follow these steps:-<\/span><\/p>\n Assumption – the given three digit integer is 289<\/span><\/p>\n Step 1:<\/strong><\/p>\n Write 289 in pairs of digits.\u00a0 Pair the digits beginning from the right. For example, 89 will be the first pair, and 2 will be left as a single digit.<\/span><\/p>\n Step 2:<\/strong><\/p>\n We’ll find the integer part (i.e., the divisor) of the square root of the single digit on the left. In this case, the square root of 1 will give us 1. Here, we will consider 1 because its square root is less than 2. This will be the digit of the importance of the resultant square root. Write it at the top as the quotient. This is the current digit.<\/span><\/p>\n Step 3:<\/strong><\/p>\n Now, we write the square of the current digit below the digit of significance and find the difference between the two (which is 1 here)\u2014bringing down the next pair of digits on the right, i.e., 89, to append to the difference 1. The resultant number is then 189. We’ll call this the new number. This will complete our first stage of finding the digit of the significance of the square root.<\/span><\/p>\n Step 4:<\/strong><\/p>\n On the left of the new number, we’ll write the double of the square root result formed till this stage. At this point, it will be just 2 (as 1\u00d72=2). Next, we need to find a digit to append to 2 so that the product of the two-digit number formed and the digit appended is just less than or equal to the new number 189.<\/span><\/p>\n Appending 7 to 2 will form 27, and 7×27 gives us 189 with a remainder of 0. 7 now becomes the current digit, and it is appended to the square root result at the top to form 17 as the final square root.<\/span><\/p>\n This method stops when the remainder is 0.<\/span><\/p>\n <\/span><\/p>\n To calculate the square roots of a given integer with an even number of digits, we follow these steps:-<\/span><\/p>\n Assumption – the given integer is 7921.<\/span><\/p>\n Step 1:<\/strong><\/p>\n We begin by writing 7921 in pairs of digits from the right. The pairs thus formed are ’79’ ’21’.<\/span><\/p>\n Step 2:<\/strong><\/p>\n Now the integer part (i.e., the divisor) of the square root of 79 is 8, and its square gives us 64. Here, we are considering 8 because its square root is less than 79. Subtracting 64 from 79 gives us 15 as a remainder. This number then becomes 15 21 when the next pair of digits is brought down. Thus, 8 is the current divisor and forms the digit of the significance of the square root result.<\/span><\/p>\n Step 3:<\/strong><\/p>\n Square root result formed till now 8X2= 16. Now, by appending 9 to 16. We are considering 9 after a method of trials and errors. We get the new number as 169, so that 9\u00d7169=1521. 9 is appended to 8, and the square root result thus formed is 89. As the remainder becomes zero, the process ends, and 89 is our desired answer.<\/span><\/p>\n [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][et_pb_text admin_label=”Related Concepts [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” hover_enabled=”0″ locked=”off” global_colors_info=”{}” sticky_enabled=”0″]<\/p>\nFinding out square roots of positive integers –<\/strong><\/h3>\n
Finding out square roots of negative integers –<\/strong><\/h3>\n
Finding out square roots of integers with an odd number of digits –<\/strong><\/h3>\n
<\/span><\/p>\nFinding out the square root of integers with even number of digits –<\/strong><\/h3>\n
<\/span><\/p>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nRelated Concepts<\/h1>\n