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In this article, we will learn about the value and derivation of the square root of 25. The value of root 25 is very easy to find because it is a perfect square. The value of <\/span>\u221a<\/span>25 equals 5. The square root of 25 is expressed or represented as \u221a25 in mathematics. The value of root 25 can be positive and negative.\u00a0 If the root of the square is not a whole number, the final result will be an irrational number. <\/span>The symbol \u2018\u221a\u2019 represents a square root and is also called \u2018radical\u2019.\u00a0<\/span><\/p>\n <\/p>\n A value expressed by x = \u221aa represents the square of any natural integer. It means that x is the square root of a. Thus, the square root of any number is equal to a number that gives the original numbers when multiplied by itself. For instance, 5 x 5 = 25, and the square root of the number 25 can be stated to be +5 or -5.<\/span><\/p>\n <\/p>\n If it’s not a perfect square, it’s an irrational number. Because 25 is a perfect square, the number is rational. This means that there will be no decimal places to the square root of 25.<\/span><\/p>\n To find the value of \u221a25 by prime factorisation, follow the steps mentioned below:<\/span><\/p>\n <\/p>\n Question 1: Find the radius of a circle if its area is 25<\/span>\u03c0 cm<\/span>2<\/span> Question 2: Find the value of \u2018x\u2019 if x<\/span>2<\/sup><\/span> = 50<\/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>\nPerfect and non-perfect squares<\/strong><\/h2>\n
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The square root of 25<\/strong><\/h2>\n
Table of the square root of numbers from 1 to 50<\/strong><\/h2>\n
\n\n
\n Number<\/b><\/td>\n Square Root<\/b><\/td>\n Number<\/b><\/td>\n Square Root<\/b><\/td>\n<\/tr>\n \n 1<\/span><\/td>\n 1<\/span><\/td>\n 26<\/span><\/td>\n 5.099<\/span><\/td>\n<\/tr>\n \n 2<\/span><\/td>\n 1.414<\/span><\/td>\n 27<\/span><\/td>\n 5.196<\/span><\/td>\n<\/tr>\n \n 3<\/span><\/td>\n 1.732<\/span><\/td>\n 28<\/span><\/td>\n 5.292<\/span><\/td>\n<\/tr>\n \n 4<\/span><\/td>\n 2<\/span><\/td>\n 29<\/span><\/td>\n 5.385<\/span><\/td>\n<\/tr>\n \n 5<\/span><\/td>\n 2.236<\/span><\/td>\n 30<\/span><\/td>\n 5.477<\/span><\/td>\n<\/tr>\n \n 6<\/span><\/td>\n 2.449<\/span><\/td>\n 31<\/span><\/td>\n 5.568<\/span><\/td>\n<\/tr>\n \n 7<\/span><\/td>\n 2.646<\/span><\/td>\n 32<\/span><\/td>\n 5.657<\/span><\/td>\n<\/tr>\n \n 8<\/span><\/td>\n 2.828<\/span><\/td>\n 33<\/span><\/td>\n 5.745<\/span><\/td>\n<\/tr>\n \n 9<\/span><\/td>\n 3<\/span><\/td>\n 34<\/span><\/td>\n 5.831<\/span><\/td>\n<\/tr>\n \n 10<\/span><\/td>\n 3.162<\/span><\/td>\n 35<\/span><\/td>\n 5.916<\/span><\/td>\n<\/tr>\n \n 11<\/span><\/td>\n 3.317<\/span><\/td>\n 36<\/span><\/td>\n 6<\/span><\/td>\n<\/tr>\n \n 12<\/span><\/td>\n 3.464<\/span><\/td>\n 37<\/span><\/td>\n 6.083<\/span><\/td>\n<\/tr>\n \n 13<\/span><\/td>\n 3.606<\/span><\/td>\n 38<\/span><\/td>\n 6.164<\/span><\/td>\n<\/tr>\n \n 14<\/span><\/td>\n 3.742<\/span><\/td>\n 39<\/span><\/td>\n 6.245<\/span><\/td>\n<\/tr>\n \n 15<\/span><\/td>\n 3.873<\/span><\/td>\n 40<\/span><\/td>\n 6.325<\/span><\/td>\n<\/tr>\n \n 16<\/span><\/td>\n 4<\/span><\/td>\n 41<\/span><\/td>\n 6.403<\/span><\/td>\n<\/tr>\n \n 17<\/span><\/td>\n 4.123<\/span><\/td>\n 42<\/span><\/td>\n 6.481<\/span><\/td>\n<\/tr>\n \n 18<\/span><\/td>\n 4.234<\/span><\/td>\n 43<\/span><\/td>\n 6.557<\/span><\/td>\n<\/tr>\n \n 19<\/span><\/td>\n 4.359<\/span><\/td>\n 44<\/span><\/td>\n 6.633<\/span><\/td>\n<\/tr>\n \n 20<\/span><\/td>\n 4.472<\/span><\/td>\n 45<\/span><\/td>\n 6.708<\/span><\/td>\n<\/tr>\n \n 21<\/span><\/td>\n 4.583<\/span><\/td>\n 46<\/span><\/td>\n 6.6.782<\/span><\/td>\n<\/tr>\n \n 22<\/span><\/td>\n 4.690<\/span><\/td>\n 47<\/span><\/td>\n 6.856<\/span><\/td>\n<\/tr>\n \n 23<\/span><\/td>\n 4.796<\/span><\/td>\n 48<\/span><\/td>\n 6.928<\/span><\/td>\n<\/tr>\n \n 24<\/span><\/td>\n 4.899<\/span><\/td>\n 49<\/span><\/td>\n 7<\/span><\/td>\n<\/tr>\n \n 25<\/span><\/td>\n 5<\/span><\/td>\n 50<\/span><\/td>\n 7.071<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Is root 25 rational or irrational?<\/strong><\/h3>\n
How to find the value of the square root of 25 by prime factorisation?<\/strong><\/h3>\n
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<\/span> 25 = 5 x 5<\/span><\/li>\n
<\/span> 25 = 5 x 5<\/span><\/li>\n
<\/span> \u221a25 = \u221a(5<\/span>2<\/sup><\/span>)<\/span>
<\/span> \u221a25 = (5)2 x \u00bd
<\/sup><\/span>\u221a25 = 5<\/span><\/li>\n<\/ol>\nSolved Question<\/strong><\/h3>\n
Solution –\u00a0<\/span>
Given, the area of the circle = 25\u03c0 cm<\/span>2<\/sup><\/span>
Now, area = \u03c0r<\/span>2<\/sup><\/span> (r is the radius of the circle)<\/span>
So,\u00a0<\/span>
\u03c0r<\/span>2 <\/span>= <\/span>25<\/span>\u03c0 cm<\/span>2<\/sup><\/span>
We get, r<\/span>2 <\/span>= <\/span>25<\/span> cm<\/span>2<\/sup><\/span>
r<\/span> = <\/span>\u221a25<\/span> cm<\/span>
\u00a0Putting the value of <\/span>\u221a25 in the above equation,\u00a0<\/span>
We get, r = <\/span>\u00b1<\/span>5 cm<\/span>
Here we will consider the positive value of 5.<\/span>
Therefore, the radius of the circle is 5 cm.<\/span><\/p>\n
Solution: Given, x<\/span>2<\/sup><\/span> = 50<\/span>
x = <\/span>\u00b1<\/span>\u221a50<\/span>
x = \u221a(2 x 5 x 5)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (considering that the positive value of root 50)<\/span>
x = 5\u221a2<\/span>
we know that \u221a2 = 1.414<\/span>
so, x = 5 (1.414)<\/span>
x = 7.07<\/span><\/p>\n
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\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