<\/b><\/p>\n
It is necessary to know what are perfect and non-perfect squares before determining the value of root 7. In the ones place of any perfect square integer, there are 1, 4, 5, 6, 9. Every number ending with 2, 3, 7 and 8 are referred to as non-perfect. Therefore, 7 is a non-perfect square, and \u221a7 is equal to 2.64575 (rounded up to 5 decimal places). This also indicates that (2.64575)^{2}<\/span>= 7. Although root 7 can have a negative value as well, in this article, we will only consider the positive value.<\/p>\n <\/p>\n <\/b><\/p>\n How do you differentiate between a rational and an irrational number? While we know that we can express a rational number in the form of \\frac{p}{q}<\/span> where<\/span> q \u2260 0<\/span>. , An irrational number cannot be expressed in this way. Any number that does not seem to terminate after the decimal point is called an irrational number. In this case, <\/span>\u221a7 is an irrational number because its value, <\/span>2.645751311064591<\/span>, doesn\u2019t terminate after the decimal, and it is a never-ending number.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n 1. Before you dive in with numbers, know that the square root of 7 would lie somewhere between the square root of two perfect square numbers.<\/span><\/p>\n 2. Find the two perfect squares before and after \u221a7, i.e., \u221a4 and \u221a9 as \u221a4 < \u221a7 < \u221a9.<\/span><\/p>\n 3. Therefore, the value of \u221a7 lies between 2 and 3.<\/span><\/p>\n 4. Now divide 7 with either 2 or 3. Here, we decided to divide 7 by 3, thereby,<\/span><\/p>\n 7 \u00f7 3 = 2.33<\/span><\/p>\n 5. Calculate the average of 2.33 and 3.<\/span><\/p>\n (2.33+3) \u00f7 2 = 2.66<\/span><\/p>\n 6. Therefore, by using the average method, we get an approximate value of \u221a7 as 2.66<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n <\/b><\/span><\/p>\n The long division method is the most widely accepted method to find the value of a square root. It not only gives the exact value of a square root but also helps you form a better understanding of numbers.<\/span><\/p>\n <\/span><\/p>\n Follow the steps below to find the value of <\/span>\u221a7 by long division method:<\/span><\/p>\n Begin to pair numbers- right to left for whole numbers and left to right for decimal numbers<\/span><\/p>\n <\/p>\n Step 1:<\/strong> Write 7, put a decimal point after it and place 3 pairs of zeros after the decimal point.<\/p>\n Step 2:<\/strong> Now group these zeros into pairs of two by placing a bar above each pair.<\/p>\n Step 3:<\/strong> Choose a number whose square gives a value below 7. In this case, the number is 2 as (2)^{2}=4<\/span>. So write 2 in the dividend and quotient place. Now, follow the traditional way of division.<\/p>\n Step 4:<\/strong> Now, bring down the pair of zeros and place the decimal in the quotient, after 2.<\/p>\n Step 5:<\/strong> Add 2 to the divisor to get 4, and now think of a number to make a two-digit number which, when multiplied by the number taken, gives a number smaller than the current dividend.<\/p>\n Step 6:<\/strong> Repeat the above steps, until you get the quotient value up to 3 decimal places. <\/p>\n <\/p>\n Question 1:<\/strong> Find the value of \u2018x\u2019 if x^{2}=28<\/span>.<\/span><\/p>\n Solution:<\/strong> Given, <\/span>x^{2}=28<\/span>.<\/p>\n x = \u221a28<\/p>\n x = (\u221a4 x \u221a7)<\/p>\n We know that \u221a4 = 2<\/p>\n so, x = 2 (\u221a7)<\/p>\n x = 2 x 2.645<\/p>\n x = 5.29<\/p>\n <\/p>\n Question 2:<\/strong> Calculate the radius of circular cardboard if its area is 22 \\mathrm{~cm}^{2}<\/span>.<\/span><\/p>\n Solution:<\/strong> We know that \\pi r^{2}<\/span><\/span>gives the area of a circle.<\/span>\u00a0<\/span><\/p>\n Given, area =22 \\mathrm{~cm}^{2}<\/span><\/span><\/p>\n so, \\pi r^{2}=22<\/span><\/span><\/p>\n \\Rightarrow \\frac{22}{7}\\times r^{2}=22<\/span><\/span><\/p>\n \\Rightarrow r^{2}=7<\/span><\/span><\/p>\n Hence, r = <\/span>\u221a7 = 2.645 cm (rounded up to 3 decimal places)<\/span><\/p>\n Therefore, the radius of the circular cardboard is 2.645cm.<\/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>\n\u221a7<\/b> is an irrational number<\/b><\/h2>\n
Finding the value of \u221a7 by the average method<\/strong>
<\/span><\/h2>\n<\/b><\/span><\/h2>\n
\u221a7 by long division method<\/b><\/span><\/h2>\n
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Root-7-01-239x300.png\")
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The value of \u221a7 = 2.645<\/p>\nExamples<\/h2>\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