{"id":2287,"date":"2021-09-29T03:46:20","date_gmt":"2021-09-29T03:46:20","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2287"},"modified":"2021-12-31T11:10:42","modified_gmt":"2021-12-31T11:10:42","slug":"square-root-of-8-value-and-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/square-root-of-8-value-and-examples\/","title":{"rendered":"Square root of 8 &#8211; value and examples"},"content":{"rendered":"<p>[et_pb_section fb_built=&#8221;1&#8243; admin_label=&#8221;Section&#8221; module_class=&#8221;mainsec&#8221; _builder_version=&#8221;4.10.4&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#e0f2fd&#8221; z_index=&#8221;1&#8243; custom_padding=&#8221;5px||5px||true|false&#8221; locked=&#8221;off&#8221; collapsed=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_row column_structure=&#8221;3_5,2_5&#8243; custom_padding_last_edited=&#8221;on|phone&#8221; _builder_version=&#8221;4.10.6&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#FFFFFF&#8221; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; custom_padding=&#8221;|51px|40px|51px|false|true&#8221; custom_padding_tablet=&#8221;&#8221; custom_padding_phone=&#8221;|40px|30px|40px|false|true&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;3_5&#8243; admin_label=&#8221;Column L&#8221; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;Acute Angles<br \/>\n&#8221; _builder_version=&#8221;4.11.3&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_text_align=&#8221;left&#8221; header_font_size=&#8221;50px&#8221; header_line_height=&#8221;1.18em&#8221; custom_padding=&#8221;|0px||4px|false|false&#8221; header_font_size_tablet=&#8221;&#8221; header_font_size_phone=&#8221;35px&#8221; header_font_size_last_edited=&#8221;on|phone&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1><strong>Square root of 8 &#8211; value and examples<\/strong><\/h1>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Text&#8221; _builder_version=&#8221;4.11.3&#8243; _module_preset=&#8221;default&#8221; text_font_size=&#8221;16px&#8221; header_2_font=&#8221;|600|||||||&#8221; header_2_text_color=&#8221;#a01414&#8243; header_3_font=&#8221;|600|||||||&#8221; custom_padding=&#8221;15px|15px||4px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<p><span style=\"font-weight: 400;\">The square root of 8 in radical form is denoted by <\/span><span style=\"font-weight: 400;\">\u221a8. <\/span><span style=\"font-weight: 400;\">The value of root 8 is an irrational number. Its value up to 4 decimal places is 2.828<\/span><span style=\"font-weight: 400;\">. The square root is a concept that equates to the undoing of the square operation, and <\/span><span style=\"font-weight: 400;\">on squaring 2.828 we are going to get a value that is almost equal to 8.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Let us first look at the concept of exponents with respect to the square root operation. For example, if we have a number \u2018a\u2019 and multiply it with itself \u2018n\u2019 number of times, then a<\/span><span style=\"font-weight: 400;\"><sup style=\"font-size: 10px;\">n<\/sup><\/span><span style=\"font-weight: 400;\"> = a x a x a \u2026.. n times<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Here, we know that we must multiply the number by itself to get its square value. Therefore, \u2018n\u2019 = 2.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Now, let \u2018a\u2019 be 4<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Then, 4<\/span><span style=\"font-weight: 400;\"><sup style=\"font-size: 10px;\">2<\/sup><\/span><span style=\"font-weight: 400;\"> = 4 x 4 = 16.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">16 is the square of 4, and upon inversing the square operation, we know that 4 is the square root of 16.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This article will tell us more about finding the square root of 8 and why it is an irrational number.\u00a0<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">How to find the square root of 8?<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">We can find the square root of 8 by using any one of the methods given below:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">By prime factorization\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">By long division\u00a0<\/span><\/li>\n<\/ul>\n<h3><span style=\"font-weight: 400;\">Prime factorization method<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">In this method, we first find the factors of 8<\/span><\/p>\n<p><span style=\"font-weight: 400;\">8 = 2 x 2 x 2\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">So, <\/span><span style=\"font-weight: 400;\">\u221a8 can be written as \u221a(2 x 2 x 2)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">( we make pairs of equal factors and pick up one factor from each pair)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Now, \u221a8 = 2\u221a2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">We know \u221a2 = 1.414.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u221a8 = 2 x 1.414 = 2.828<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">Long division method<\/span><\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">We can find the square root of 8 by first adding zeros to the right of the decimal.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">We know that the square of 2 is 4 and the square of 3 is 9, so we will take the number with a square less than 8 and place it as a divisor.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Take the number 2, as the new divisor and quotient and 8 as the dividend. Then we\u00a0 divide it with\u00a0 the next remaining number below the extreme left.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Bring down the next pair of numbers to the right of the remainder\u00a0under the next bar.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">To calculate the divisor, multiply the previous quotient by 2 and choose a number that is less than or equal to the new dividend.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">By repeating the above steps until we get zero remainder, we can find the square root of 8 by the long division method.<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Square-root-of-8-01-229x300.png\" width=\"298\" height=\"390\" alt=\"\" class=\"wp-image-3430 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Square-root-of-8-01-229x300.png 229w, https:\/\/eistudymaterial.s3.amazonaws.com\/Square-root-of-8-01.png 289w\" sizes=\"(max-width: 298px) 100vw, 298px\" \/><\/p>\n<h2><span style=\"font-weight: 400;\">Root 8 is an irrational number<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Let us look at the value of root 8, <\/span><span style=\"font-weight: 400;\">\u221a8 = <\/span><span style=\"font-weight: 400;\">2.82842712474619\u2026\u2026<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The numbers after the decimal are non-terminating and non-repeating, and we cannot write the value of <\/span><span style=\"font-weight: 400;\">\u221a8 in the form of p\/q (<\/span><span style=\"font-weight: 400;\">where p and q are integers and q not equal to 0)<\/span><span style=\"font-weight: 400;\">. Hence, the value of root 8 is irrational. It would have been rational if the digits after the decimal place were terminating or repetitive.\u00a0<\/span><\/p>\n<p>[\/et_pb_text][\/et_pb_column][et_pb_column type=&#8221;2_5&#8243; module_id=&#8221;stickysideR&#8221; admin_label=&#8221;Column R&#8221; _builder_version=&#8221;4.10.4&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#fdefe0&#8243; custom_padding=&#8221;25px|25px|25px|25px|true|true&#8221; sticky_position=&#8221;top&#8221; sticky_offset_top=&#8221;-280px&#8221; sticky_limit_top=&#8221;row&#8221; sticky_limit_bottom=&#8221;row&#8221; sticky_position_tablet=&#8221;none&#8221; sticky_position_phone=&#8221;none&#8221; sticky_position_last_edited=&#8221;on|desktop&#8221; sticky_limit_bottom_tablet=&#8221;&#8221; sticky_limit_bottom_phone=&#8221;&#8221; sticky_limit_bottom_last_edited=&#8221;on|phone&#8221; border_radii=&#8221;on|15px|15px|15px|15px&#8221; box_shadow_style=&#8221;preset3&#8243; global_colors_info=&#8221;{}&#8221;][et_pb_image src=&#8221;https:\/\/eistudymaterial.s3.amazonaws.com\/1080&#215;1080.png&#8221; alt=&#8221;Free Trial banner&#8221; title_text=&#8221;Mindspark Free Trial Banner&#8221; url=&#8221;https:\/\/mindspark.in\/free-trial&#8221; align=&#8221;center&#8221; module_class=&#8221;adsimg&#8221; _builder_version=&#8221;4.11.1&#8243; _module_preset=&#8221;default&#8221; custom_padding=&#8221;||||false|false&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221; transform_styles__hover_enabled=&#8221;on|hover&#8221; transform_scale__hover_enabled=&#8221;on|hover&#8221; transform_translate__hover_enabled=&#8221;on|desktop&#8221; transform_rotate__hover_enabled=&#8221;on|desktop&#8221; transform_skew__hover_enabled=&#8221;on|desktop&#8221; transform_origin__hover_enabled=&#8221;on|desktop&#8221; transform_scale__hover=&#8221;102%|102%&#8221;][\/et_pb_image][et_pb_text admin_label=&#8221;Explore Other Topics<br \/>\n&#8221; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_font_size=&#8221;25px&#8221; text_orientation=&#8221;center&#8221; custom_margin=&#8221;0px||0px||true|false&#8221; custom_padding=&#8221;8px|15px|0px|15px|false|true&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Explore Other Topics<\/h1>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.10.7&#8243; _module_preset=&#8221;default&#8221; text_line_height=&#8221;2.2em&#8221; link_font_size=&#8221;16px&#8221; custom_margin=&#8221;||0px||false|false&#8221; custom_padding=&#8221;10px|15px|10px|28px|true|false&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div>\n<div class=\"trr\"><a href=\"http:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#geometry\" class=\"otherc\">Geometry<\/a><\/div>\n<div class=\"trr\"><a href=\"http:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#trigonometry\" class=\"otherc\">Trigonometry<\/a><\/div>\n<div class=\"trr\"><a href=\"http:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#operations\" class=\"otherc\">Operations<\/a><\/div>\n<div class=\"trr\"><a href=\"http:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#numbers\" class=\"otherc\">Numbers<\/a><\/div>\n<\/div>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Related Concepts<br \/>\n&#8221; _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_font_size=&#8221;25px&#8221; text_orientation=&#8221;center&#8221; custom_margin=&#8221;0px||0px||true|false&#8221; custom_padding=&#8221;8px|15px|0px|15px|false|true&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Related Concepts<\/h1>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; text_line_height=&#8221;2.2em&#8221; link_font_size=&#8221;16px&#8221; custom_margin=&#8221;||0px||false|false&#8221; custom_padding=&#8221;10px|15px|10px|28px|true|false&#8221; hover_enabled=&#8221;0&#8243; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221; sticky_enabled=&#8221;0&#8243;]<\/p>\n<div>\n<div class=\"trr\"><a href=\"https:\/\/mindspark.in\/studymaterial\/math-concepts\/the-square-root-of-numbers-between-1-to-50\/\" class=\"otherc\">Square root from 1 to 50<\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/mindspark.in\/studymaterial\/math-concepts\/root-4-value-meaning-and-examples-2\/\" class=\"otherc\">Root 4 <\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/mindspark.in\/studymaterial\/math-concepts\/square-root-of-12-value-simplification-and-examples\/\" class=\"otherc\">Square root of 12<\/a><\/div>\n<\/div>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=&#8221;Row for space&#8221; 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_module_preset=&#8221;default&#8221; background_color=&#8221;#fff7d6&#8243; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; height=&#8221;134px&#8221; custom_margin=&#8221;||50px||false|false&#8221; custom_padding=&#8221;12px||12px||true|false&#8221; border_radii=&#8221;on|11px|11px|11px|11px&#8221; locked=&#8221;off&#8221; collapsed=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_image src=&#8221;http:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/calloutImage.png&#8221; title_text=&#8221;calloutImage&#8221; show_bottom_space=&#8221;off&#8221; admin_label=&#8221;Image&#8221; module_class=&#8221;img1&#8243; _builder_version=&#8221;4.10.8&#8243; _module_preset=&#8221;default&#8221; width=&#8221;25px&#8221; height=&#8221;60px&#8221; custom_padding=&#8221;2px||2px||true|false&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][et_pb_text module_class=&#8221;ftstyle&#8221; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; text_orientation=&#8221;center&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div class=\"ffmanage\">\n<div class=\"textmanagestyle\">\n<div class=\"fone\">\n<p>Ready to get started ?<\/p>\n<\/div>\n<div class=\"sone\">\n<p class=\"ffbtn\"><a href=\"https:\/\/mindspark.in\/free-trial\">Start Free Trial<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>[\/et_pb_text][et_pb_image src=&#8221;http:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/down-circle.png&#8221; title_text=&#8221;down-circle&#8221; show_bottom_space=&#8221;off&#8221; align=&#8221;right&#8221; module_class=&#8221;img2&#8243; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; width=&#8221;44px&#8221; height=&#8221;18px&#8221; custom_padding=&#8221;2px||2px||true|false&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=&#8221;FAQ Row&#8221; _builder_version=&#8221;4.10.8&#8243; _module_preset=&#8221;default&#8221; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; custom_padding=&#8221;|40px||40px|false|true&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;FAQ&#8221; module_class=&#8221;faqstyl&#8221; _builder_version=&#8221;4.11.3&#8243; _module_preset=&#8221;default&#8221; text_font_size=&#8221;16px&#8221; header_font=&#8221;|700|||||||&#8221; header_text_align=&#8221;center&#8221; header_line_height=&#8221;2.5em&#8221; background_color=&#8221;#dbedc6&#8243; max_width=&#8221;80%&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;||||false|false&#8221; custom_padding=&#8221;30px|25px|30px|25px|true|true&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Frequently Asked Questions<\/h1>\n<p><span style=\"font-weight: 400;\"><strong>1.<\/strong> What is the value of <\/span><span style=\"font-weight: 400;\">\u221a8 up to 4 decimal places?<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>Ans:<\/strong> The value of root 8 up to 4 decimal places is 2.8284<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>2.<\/strong> Is <\/span><span style=\"font-weight: 400;\">\u221a8 an irrational or rational number?<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>Ans:<\/strong> \u221a8 is an irrational number because the value of \u221a8 doesn\u2019t terminate and keeps on extending.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>3.<\/strong> Express root 8 in exponential form.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>Ans:<\/strong> The exponential form of root 8 is (8)<\/span><span style=\"font-weight: 400;\"><sup style=\"font-size: 10px;\">1\/2<\/sup>.<\/span>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The square root of 64 is 8, and we can calculate this by the prime factorisation method. Let us calculate the value of root 64 to prove it is a rational number. <\/p>\n","protected":false},"author":7,"featured_media":0,"parent":714,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Square root of 8 - value and examples - mydomain<\/title>\n<meta name=\"description\" content=\"The square root of 64 is 8, and we can calculate this by the prime factorisation method. 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