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The square root of 20 value<\/strong><\/h2>\nThe square root of a number is the value that, when multiplied by itself, gives the original value. It is the inverse of squares. Root 20 is denoted as \u221a20 in its radical form. Its square root, rounded up to three decimal spaces, is 4.472. The value of \u221a20 can also be negative, that is -4.472. But in this article we will be considering only its positive value.<\/span><\/p>\nIs root 20 an irrational number?<\/strong><\/h2>\nThe value of root 20 is an irrational number because the decimal form of \u221a20 is non terminating, and at the same time, it is non-recurring. That means none of its digits in the decimal space ever repeat themselves, nor can we see a pattern in their appearance.\u00a0<\/span><\/p>\nNow, we’re going to look at the methods of finding out the value of \u221a20.<\/span><\/p>\n <\/p>\n
Finding the value of \u221a20 using the long division method:-<\/strong><\/h2>\n<\/strong><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Square-root-of-20-Value-Derivation-and-Examples-01-250x300.png\")
<\/strong><\/p>\n<\/strong><\/p>\nThe long division method is one of the most convenient ways of determining the root values of numbers. Here, we’ll follow these steps to find the value of root 20 by long division method:-<\/span><\/p>\nStep 1:<\/strong><\/p>\nMake a pair of digits (by placing a bar over it) from the unit’s place.<\/span><\/p>\nStep 2:<\/strong><\/p>\nWe’ll now have to find a number such that when it is multiplied by itself, the product is less than or equal to 20.<\/span><\/p>\nWe know that 4\u00b2 gives us 16, and 16 is less than 20. So it becomes our divisor.\u00a0<\/span><\/p>\nStep 3:<\/strong><\/p>\nNext, we’ll place a decimal point and a pair of zeros next to it and continue our division. Now, we multiply the quotient by 2, and the product becomes the starting digit of our next divisor.<\/span><\/p>\nStep 4:<\/strong><\/p>\nNow we’ll have to choose a number in the unit’s place for the new divisor such that its product with a number is less than or equal to 400.<\/span><\/p>\nSo, the closest multiplication we’re left with is 84 \u00d7 4 = 336<\/span><\/p>\nStep 5:<\/strong><\/p>\nWe bring down the next pair of zeros and add 4 to the quotient, and we get the starting digit of the new divisor.<\/span><\/p>\nStep 6:<\/strong><\/p>\nNow, we choose a number in the unit’s place for the new divisor such that its product with a number is less than or equal to 6400. 6209 is the nearest number possible, leaving us with a remainder of 191.<\/span><\/p>\nStep 7:<\/strong><\/p>\nMore pairs of zeros are added, and the process is repeated to find the new divisor and product as in step 2.<\/span><\/p>\n <\/p>\n
Simplification of root 20<\/strong><\/h2>\nIf you think that long division is time-consuming, you can find the value of \u221a20 by simplification. But, first, you must find the prime factors of 20.\u00a0<\/span><\/p>\n20 = 2 x 2 x 5<\/span><\/p>\nNow, we can see that we cannot pair the number 5. Therefore, 20 is a non-perfect square. Adding root on both sides.<\/span><\/p>\nWe get, \u221a20 = \u221a(2 x 2 x 5)<\/span><\/p>\nNow, since we can make a pair of the number 2, we can take it out from the root but leave the number 5 within the root.\u00a0<\/span><\/p>\n\u221a20 = \u221a(2 x 2 x 5)<\/span><\/p>\n\u221a20 = 2\u221a5<\/span><\/p>\n\u221a20 = 2 x 2.236 because \u221a5 = 2.236<\/span><\/p>\nSo, \u221a20 = 4.472<\/span><\/p>\nSolved Question<\/strong><\/h3>\nQuestion 1: Find the value of \u2018x\u2019 if x<\/span>\u00b2<\/span> = 20<\/span>
Solution: Given, x<\/span>\u00b2<\/span> = 20<\/span>
x = <\/span>\u221a20<\/span>
x = \u221a(2 x 2 x 5)<\/span>
x = \u221a(4 x 5)<\/span>
we know that \u221a4 = 2<\/span>
so, x = 2 (\u221a5)<\/span>
x = 2 x<\/span> 2.236<\/span>
x = 4.472<\/span><\/p>\nQuestion 2: Calculate the length of the diagonal of a square sheet if its sides are <\/span>\u221a<\/span>20cm each.\u00a0<\/span>
Solution: Side \u2018s\u2019 of the square sheet = <\/span>\u221a<\/span>20cm<\/span>
By applying Pythagoras theorem, the diagonal of square = <\/span>\u221a2 x s<\/span>\u00a0<\/span>
= \u221a<\/span>2<\/span> x <\/span>\u221a<\/span>20<\/span>
= 1.732 x 4.472 cm<\/span>
= 7.74 cm<\/span>
Therefore, the diagonal of the square sheet is 7.74 cm.<\/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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Square and Square roots<\/a><\/div>\nRoot 10<\/a><\/div>\n
Is root 20 an irrational number?<\/strong><\/h2>\nThe value of root 20 is an irrational number because the decimal form of \u221a20 is non terminating, and at the same time, it is non-recurring. That means none of its digits in the decimal space ever repeat themselves, nor can we see a pattern in their appearance.\u00a0<\/span><\/p>\nNow, we’re going to look at the methods of finding out the value of \u221a20.<\/span><\/p>\n <\/p>\n
Finding the value of \u221a20 using the long division method:-<\/strong><\/h2>\n<\/strong><\/p>\n<\/strong><\/p>\n<\/strong><\/p>\nThe long division method is one of the most convenient ways of determining the root values of numbers. Here, we’ll follow these steps to find the value of root 20 by long division method:-<\/span><\/p>\nStep 1:<\/strong><\/p>\nMake a pair of digits (by placing a bar over it) from the unit’s place.<\/span><\/p>\nStep 2:<\/strong><\/p>\nWe’ll now have to find a number such that when it is multiplied by itself, the product is less than or equal to 20.<\/span><\/p>\nWe know that 4\u00b2 gives us 16, and 16 is less than 20. So it becomes our divisor.\u00a0<\/span><\/p>\nStep 3:<\/strong><\/p>\nNext, we’ll place a decimal point and a pair of zeros next to it and continue our division. Now, we multiply the quotient by 2, and the product becomes the starting digit of our next divisor.<\/span><\/p>\nStep 4:<\/strong><\/p>\nNow we’ll have to choose a number in the unit’s place for the new divisor such that its product with a number is less than or equal to 400.<\/span><\/p>\nSo, the closest multiplication we’re left with is 84 \u00d7 4 = 336<\/span><\/p>\nStep 5:<\/strong><\/p>\nWe bring down the next pair of zeros and add 4 to the quotient, and we get the starting digit of the new divisor.<\/span><\/p>\nStep 6:<\/strong><\/p>\nNow, we choose a number in the unit’s place for the new divisor such that its product with a number is less than or equal to 6400. 6209 is the nearest number possible, leaving us with a remainder of 191.<\/span><\/p>\nStep 7:<\/strong><\/p>\nMore pairs of zeros are added, and the process is repeated to find the new divisor and product as in step 2.<\/span><\/p>\n <\/p>\n
Simplification of root 20<\/strong><\/h2>\nIf you think that long division is time-consuming, you can find the value of \u221a20 by simplification. But, first, you must find the prime factors of 20.\u00a0<\/span><\/p>\n20 = 2 x 2 x 5<\/span><\/p>\nNow, we can see that we cannot pair the number 5. Therefore, 20 is a non-perfect square. Adding root on both sides.<\/span><\/p>\nWe get, \u221a20 = \u221a(2 x 2 x 5)<\/span><\/p>\nNow, since we can make a pair of the number 2, we can take it out from the root but leave the number 5 within the root.\u00a0<\/span><\/p>\n\u221a20 = \u221a(2 x 2 x 5)<\/span><\/p>\n\u221a20 = 2\u221a5<\/span><\/p>\n\u221a20 = 2 x 2.236 because \u221a5 = 2.236<\/span><\/p>\nSo, \u221a20 = 4.472<\/span><\/p>\nSolved Question<\/strong><\/h3>\nQuestion 1: Find the value of \u2018x\u2019 if x<\/span>\u00b2<\/span> = 20<\/span>
Solution: Given, x<\/span>\u00b2<\/span> = 20<\/span>
x = <\/span>\u221a20<\/span>
x = \u221a(2 x 2 x 5)<\/span>
x = \u221a(4 x 5)<\/span>
we know that \u221a4 = 2<\/span>
so, x = 2 (\u221a5)<\/span>
x = 2 x<\/span> 2.236<\/span>
x = 4.472<\/span><\/p>\nQuestion 2: Calculate the length of the diagonal of a square sheet if its sides are <\/span>\u221a<\/span>20cm each.\u00a0<\/span>
Solution: Side \u2018s\u2019 of the square sheet = <\/span>\u221a<\/span>20cm<\/span>
By applying Pythagoras theorem, the diagonal of square = <\/span>\u221a2 x s<\/span>\u00a0<\/span>
= \u221a<\/span>2<\/span> x <\/span>\u221a<\/span>20<\/span>
= 1.732 x 4.472 cm<\/span>
= 7.74 cm<\/span>
Therefore, the diagonal of the square sheet is 7.74 cm.<\/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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Square and Square roots<\/a><\/div>\nRoot 10<\/a><\/div>\n
Now, we’re going to look at the methods of finding out the value of \u221a20.<\/span><\/p>\n <\/p>\n <\/strong><\/p>\n <\/strong><\/p>\n The long division method is one of the most convenient ways of determining the root values of numbers. Here, we’ll follow these steps to find the value of root 20 by long division method:-<\/span><\/p>\n Step 1:<\/strong><\/p>\n Make a pair of digits (by placing a bar over it) from the unit’s place.<\/span><\/p>\n Step 2:<\/strong><\/p>\n We’ll now have to find a number such that when it is multiplied by itself, the product is less than or equal to 20.<\/span><\/p>\n We know that 4\u00b2 gives us 16, and 16 is less than 20. So it becomes our divisor.\u00a0<\/span><\/p>\n Step 3:<\/strong><\/p>\n Next, we’ll place a decimal point and a pair of zeros next to it and continue our division. Now, we multiply the quotient by 2, and the product becomes the starting digit of our next divisor.<\/span><\/p>\n Step 4:<\/strong><\/p>\n Now we’ll have to choose a number in the unit’s place for the new divisor such that its product with a number is less than or equal to 400.<\/span><\/p>\n So, the closest multiplication we’re left with is 84 \u00d7 4 = 336<\/span><\/p>\n Step 5:<\/strong><\/p>\n We bring down the next pair of zeros and add 4 to the quotient, and we get the starting digit of the new divisor.<\/span><\/p>\n Step 6:<\/strong><\/p>\n Now, we choose a number in the unit’s place for the new divisor such that its product with a number is less than or equal to 6400. 6209 is the nearest number possible, leaving us with a remainder of 191.<\/span><\/p>\n Step 7:<\/strong><\/p>\n More pairs of zeros are added, and the process is repeated to find the new divisor and product as in step 2.<\/span><\/p>\n <\/p>\n If you think that long division is time-consuming, you can find the value of \u221a20 by simplification. But, first, you must find the prime factors of 20.\u00a0<\/span><\/p>\n 20 = 2 x 2 x 5<\/span><\/p>\n Now, we can see that we cannot pair the number 5. Therefore, 20 is a non-perfect square. Adding root on both sides.<\/span><\/p>\n We get, \u221a20 = \u221a(2 x 2 x 5)<\/span><\/p>\n Now, since we can make a pair of the number 2, we can take it out from the root but leave the number 5 within the root.\u00a0<\/span><\/p>\n \u221a20 = \u221a(2 x 2 x 5)<\/span><\/p>\n \u221a20 = 2\u221a5<\/span><\/p>\n \u221a20 = 2 x 2.236 because \u221a5 = 2.236<\/span><\/p>\n So, \u221a20 = 4.472<\/span><\/p>\n Question 1: Find the value of \u2018x\u2019 if x<\/span>\u00b2<\/span> = 20<\/span> Question 2: Calculate the length of the diagonal of a square sheet if its sides are <\/span>\u221a<\/span>20cm each.\u00a0<\/span> [\/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 the value of \u221a20 using the long division method:-<\/strong><\/h2>\n
<\/strong><\/p>\nSimplification of root 20<\/strong><\/h2>\n
Solved Question<\/strong><\/h3>\n
Solution: Given, x<\/span>\u00b2<\/span> = 20<\/span>
x = <\/span>\u221a20<\/span>
x = \u221a(2 x 2 x 5)<\/span>
x = \u221a(4 x 5)<\/span>
we know that \u221a4 = 2<\/span>
so, x = 2 (\u221a5)<\/span>
x = 2 x<\/span> 2.236<\/span>
x = 4.472<\/span><\/p>\n
Solution: Side \u2018s\u2019 of the square sheet = <\/span>\u221a<\/span>20cm<\/span>
By applying Pythagoras theorem, the diagonal of square = <\/span>\u221a2 x s<\/span>\u00a0<\/span>
= \u221a<\/span>2<\/span> x <\/span>\u221a<\/span>20<\/span>
= 1.732 x 4.472 cm<\/span>
= 7.74 cm<\/span>
Therefore, the diagonal of the square sheet is 7.74 cm.<\/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
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