The root of a numeric value ‘x’ is equal to another numeric value, when multiplied by itself ‘n’ number of times, equals to the numeric value ‘x’ for which we are finding the root. So, we can also say that the square root of a number is just the inverse of squaring it. In this article, we will learn how to calculate the value of <\/span>root 5<\/b>.<\/span><\/p>\n Let us look at the root in correlation with power.<\/span><\/p>\n Consider the number’ a’ and a natural number ‘x.’\u00a0<\/span><\/p>\n Then, a^x,<\/span>\u00a0= a x a x a \u2026\u2026 (multiplied ‘x’ number of times)<\/span><\/p>\n If the value of \u2018x\u2019 is 2 and \u2018a\u2019 is 4, then 4<\/span>\u00b2<\/span> = 4 x 4 = 16<\/span><\/p>\n This means, ‘4 raised to <\/span>the<\/span> power 2′ is 16.<\/span><\/p>\n Now, the root is the inverse of power. Therefore, we can also see that 4, when multiplied by itself, yields 16. Hence, if 16 is the square of 4 then 4 is also the square root of 16.<\/span><\/p>\n We can confirm that amidst the long list of irrational numbers, it also\u00a0includes square root 5. The root of 5 cannot be represented as a fraction, and it has an endless number of decimals places. Therefore, deeming it to be an <\/span>irrational number<\/b>.<\/span><\/p>\n The\u00a0value of the square root of 5, reduced to 10 decimal places is 2.2360679774\u2026<\/span><\/p>\n To determine a number’s square root, we generally verify whether it is a perfect square or not. The value of perfect squares is easy to locate, but we have to apply the long division method to get a root value for non-perfect squares.\u00a0<\/span><\/p>\n For example, a number like 2, 3, 5, 20, etc. is not a perfect square; however, 4, 9, 25 etc., are perfect squares, giving a whole number when calculating their root.<\/span><\/p>\n Step 1<\/strong>: Put a bar on every pair of numerals starting from right to left. Since we have\u00a0an odd number of digits, the extreme left single digit, i.e., 5, has a bar as well.<\/span><\/p>\n Step 2<\/strong>: Think of a number whose square is less than or equal to 5. In this case, we have 2 as its square is equal to 4.<\/span><\/p>\n Step 3<\/strong>: Take the number 2, as the new divisor and quotient. Now, divide to the next remaining number below the extreme left.<\/span><\/p>\n Step 4:<\/strong> Bring down the next pair of numbers to the right of the remainder\u00a0under the next bar.<\/span><\/p>\n Step 5<\/strong>: To calculate the divisor, multiply the previous quotient by 2 and choose a number such that the number is less than or equal to the new dividend.<\/span><\/p>\n Step 6<\/strong>: Keep repeating steps 2, 3, 4 and 5 until the remainder is 0 or repetitive.<\/span><\/p>\n Step 7:<\/strong> The quotient you thus obtain will be the value of the <\/span>square root by long division method<\/b>.\u00a0<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Thus, the <\/span>root 5 value <\/b>up to 2 decimal places us 2.24<\/span><\/p>\n To represent <\/span>\u221a5 on the number line, consider d<\/span>rawing a number line as drawn in the image. Now, mark a point at 2 units as A. Draw a perpendicular AX at A. then cut off an arc AB = 1 unit<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Now, we have OA = 2 units and AB = 1 unit<\/span><\/p>\n Using Pythagoras theorem,<\/span><\/p>\n OB<\/span>2<\/span> = AB\u00b2<\/span>\u00a0<\/span>+ OA<\/span>\u00b2<\/span><\/p>\n OB<\/span>2<\/span> = 2<\/span>\u00b2<\/span> + 1<\/span>\u00b2<\/span><\/p>\n OB<\/span>2<\/span> = 5<\/span><\/p>\n OB = <\/span>\u221a5<\/span><\/p>\n Now, since OB is equal to root 5, by taking O as the centre, draw an arc that cuts the number line at C. Clearly, OC = OB = \u221a5<\/span><\/p>\n Hence, point C represents <\/span>root 5 on number line.<\/b><\/p>\n <\/p>\n Example 1:<\/b> Prove that <\/span>root 5 is irrational.<\/b><\/p>\n To prove the above statement, we must assume that \u221a5 is a rational number, i.e., we can express it as p\/q <\/span> here p and q are co-prime integers, and q\u22600<\/span><\/p>\n Squaring both the sides, we get,<\/span> p\u00b2\/5 = q\u00b2<\/span><\/p>\n So, if 5 divides p, then p is a multiple of 5.<\/span><\/p>\n \u21d2<\/span> p = 5m<\/span> So, p\/q is not a rational number<\/span><\/p>\n Hence proved, \u221a5 is an <\/span>irrational number<\/b>.<\/span><\/p>\n <\/p>\n Example 2:<\/b> Calculate the value of <\/span>1\/<\/span>\u221a5<\/span><\/p>\n By rationalizing the denominator, we can find the value of <\/span>1<\/span>5<\/span><\/p>\n So,<\/span><\/p>\n = (<\/span>1\/<\/span>\u221a5)<\/span>* (<\/span>\u221a5\/<\/span>\u221a5)<\/span><\/p>\n = (<\/span>1* <\/span>\u221a5) \/ (<\/span>5<\/span>* \u221a5)<\/span><\/p>\n = <\/span>\u221a5 \/ <\/span>(<\/span>\u221a5<\/span>)\u00b2<\/span><\/p>\n We know that the <\/span>square of root 5<\/b>, i.e., <\/span>root 5 into root 5 is equal to<\/b> 5<\/span><\/p>\n = <\/span>\u221a5\/<\/span>5<\/span><\/p>\n Therefore, the value of <\/span>1\/root 5 is equal to<\/b> \u221a5\/<\/span>5<\/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” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=”Row for space” _builder_version=”4.10.6″ _module_preset=”default” locked=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.11″ _module_preset=”default” global_colors_info=”{}”][et_pb_divider show_divider=”off” _builder_version=”4.10.4″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_divider][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ admin_label=”banner and faq Section” module_class=”mainsec2″ _builder_version=”4.10.4″ _module_preset=”default” custom_padding=”40px||0px||false|false” global_colors_info=”{}”][et_pb_row use_custom_gutter=”on” gutter_width=”1″ make_equal=”on” disabled_on=”on|on|off” admin_label=”banner Row” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fff7d6″ width=”100%” max_width=”1310px” height=”134px” custom_margin=”||50px||false|false” custom_padding=”12px||12px||true|false” border_radii=”on|11px|11px|11px|11px” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_image src=”http:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/calloutImage.png” title_text=”calloutImage” show_bottom_space=”off” admin_label=”Image” module_class=”img1″ _builder_version=”4.10.8″ _module_preset=”default” width=”25px” height=”60px” custom_padding=”2px||2px||true|false” global_colors_info=”{}”][\/et_pb_image][et_pb_text module_class=”ftstyle” _builder_version=”4.9.10″ _module_preset=”default” text_orientation=”center” global_colors_info=”{}”]<\/p>\n<\/h2>\n
How can you find the value of root 5?<\/strong><\/h2>\n
<\/h2>\n
How to find the square root by division method?<\/b><\/h3>\n
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Root-5-02-300x117.png\")
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Root-5-01-224x300.png\")
<\/span><\/p>\n<\/h2>\n
Represent root 5 on number line<\/strong><\/h3>\n
<\/span><\/p>\nExamples<\/strong><\/h3>\n
<\/span>\u21d2<\/span> \u221a5 = p\/q<\/span><\/p>\n
<\/span>\u21d2<\/span>5 = p\u00b2\/q\u00b2<\/span>
<\/span>\u21d2<\/span>5q\u00b2 = p\u00b2 \u2014\u2014\u2014\u2014\u2014\u2013(i)<\/span><\/p>\n
<\/span>\u21d2<\/span> p\u00b2 = 25m\u00b2 \u2014\u2014\u2014\u2014-(ii)<\/span>
<\/span>From equations (i) and (ii), we get,<\/span>
<\/span>5q\u00b2 = 25m\u00b2<\/span>
<\/span>\u21d2<\/span> q\u00b2 = 5m\u00b2<\/span>
<\/span>\u21d2<\/span> q\u00b2 is a multiple of 5<\/span>
<\/span>therefore, q is also a multiple of 5<\/span>
<\/span>Hence, the common factor of p and q is 5.\u00a0<\/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