{"id":2245,"date":"2021-09-28T13:04:21","date_gmt":"2021-09-28T13:04:21","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2245"},"modified":"2021-12-31T11:17:38","modified_gmt":"2021-12-31T11:17:38","slug":"square-root-of-625-value-and-derivation","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/square-root-of-625-value-and-derivation\/","title":{"rendered":"Square root of 625 – Value and Derivation"},"content":{"rendered":"

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Square root of 625 – Value and Derivation<\/strong><\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.11.3″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” header_3_text_color=”#777777″ custom_padding=”15px|15px||4px|false|false” global_colors_info=”{}”]<\/p>\n

In this article, we will learn about the square root of 625, its value and methods to derive it. Then we will solve some questions involving root 625 and learn the mathematical applications of square root.<\/p>\n

We know that the value of square roots of perfect square numbers is very easy to find. Now, 625 is a perfect square number with 25 as its square root. The square root of 625 is expressed or represented as \u221a625 in the radical form in mathematics. Another form of expressing the square root includes the exponential form, i.e., (625)\u00bd<\/sup> or (625)0.5<\/sup>.<\/p>\n

What is the value of \u221a625?<\/strong><\/h2>\n

In mathematics, we get the square of a number by multiplication of the number by itself. This is also known as raising a number to the power of 2. If x is a number, its square will be equal to x raised to the power 2, i.e., x2<\/sup>.<\/p>\n

Now, we know that 25 x 25 = 625, so the value of \u221a625 is 25. This also has a negative value, but we will only consider the positive value.<\/p>\n

How to find the value of the square root of 625 by prime factorisation?<\/strong><\/h3>\n

To find the value of \u221a625 by prime factorisation, follow the steps mentioned below:<\/p>\n

    \n
  1. First, calculate the prime factors of 625 and write them down.
    625 = 5 x 5 x 5 x 5<\/li>\n
  2. Group these prime factors in a pair of two factors each.
    625 = 52<\/sup> x 52<\/sup><\/li>\n
  3. Add a square root on both sides.
    \u221a625 = \u221a(52<\/sup> x 52<\/sup>)
    \u221a625 = \u221a(5 x 5)2
    <\/sup>\u00a0\u221a625 = (5 x 5)2 x \u00bd
    <\/sup>\u221a625 = 25<\/li>\n<\/ol>\n

    In a similar way the square root of 625 can also be written as -25. The mathematical form:\u00a0 (-25) x (-25) =625. As the product of two(or even number) of negatives yields a positive value.<\/p>\n

    Finding the value of root 625 by long division<\/strong><\/h2>\n

    <\/strong><\/p>\n

    \"\"<\/strong><\/p>\n

    <\/strong><\/p>\n

      \n
    1. As shown in the image, write 625. Start by placing a bar above it, grouping the number in pairs of two digits from the right. The left unpaired number can be regarded as a single entity. For instance, for the number 625, 25 has one bar above it, and 6 has the second.<\/li>\n
    2. We know that digit 2’s square root is 4. Therefore, given that 2 is the quotient and divisor, the remainder equals 2.<\/li>\n
    3. Now, we’re going to bring down the next two numbers as a dividend, i.e. 25, and add 2 to our next divisor, i.e. 2+2 =4.<\/li>\n
    4. Select a number for the unit place of the divisor to yield 225 or a smaller number closest to 225 when multiplied by the new divisor. The number is 45 since 45 x 5 = 225 here.<\/li>\n
    5. Since the final remainder is zero, the two-digit quotient we get is 25 and it is the final value, i.e, square root of 625.<\/li>\n<\/ol>\n

      Is root 625 rational or irrational?<\/strong><\/h3>\n

      625 is the perfect square of +25 and -25. Both of which can be represented in the form of p\/q. Where p and q are integers and q is not equal to 0.<\/p>\n

      Therefore \u221a625 is a rational number.<\/p>\n

      Table of the square root of numbers from 1 to 50<\/strong><\/h2>\n

      The table below gives the value (positive) of square roots from 1 to 50 up to 3 decimal places. Keep it handy while solving mathematical problems.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
      Number<\/strong><\/td>\nSquare Root<\/strong><\/td>\nNumber<\/strong><\/td>\nSquare Root<\/strong><\/td>\n<\/tr>\n
      1<\/td>\n1<\/td>\n26<\/td>\n5.099<\/td>\n<\/tr>\n
      2<\/td>\n1.414<\/td>\n27<\/td>\n5.196<\/td>\n<\/tr>\n
      3<\/td>\n1.732<\/td>\n28<\/td>\n5.292<\/td>\n<\/tr>\n
      4<\/td>\n2<\/td>\n29<\/td>\n5.385<\/td>\n<\/tr>\n
      5<\/td>\n2.236<\/td>\n30<\/td>\n5.477<\/td>\n<\/tr>\n
      6<\/td>\n2.449<\/td>\n31<\/td>\n5.568<\/td>\n<\/tr>\n
      7<\/td>\n2.646<\/td>\n32<\/td>\n5.657<\/td>\n<\/tr>\n
      8<\/td>\n2.828<\/td>\n33<\/td>\n5.745<\/td>\n<\/tr>\n
      9<\/td>\n3<\/td>\n34<\/td>\n5.831<\/td>\n<\/tr>\n
      10<\/td>\n3.162<\/td>\n35<\/td>\n5.916<\/td>\n<\/tr>\n
      11<\/td>\n3.317<\/td>\n36<\/td>\n6<\/td>\n<\/tr>\n
      12<\/td>\n3.464<\/td>\n37<\/td>\n6.083<\/td>\n<\/tr>\n
      13<\/td>\n3.606<\/td>\n38<\/td>\n6.164<\/td>\n<\/tr>\n
      14<\/td>\n3.742<\/td>\n39<\/td>\n6.245<\/td>\n<\/tr>\n
      15<\/td>\n3.873<\/td>\n40<\/td>\n6.325<\/td>\n<\/tr>\n
      16<\/td>\n4<\/td>\n41<\/td>\n6.403<\/td>\n<\/tr>\n
      17<\/td>\n4.123<\/td>\n42<\/td>\n6.481<\/td>\n<\/tr>\n
      18<\/td>\n4.234<\/td>\n43<\/td>\n6.557<\/td>\n<\/tr>\n
      19<\/td>\n4.359<\/td>\n44<\/td>\n6.633<\/td>\n<\/tr>\n
      20<\/td>\n4.472<\/td>\n45<\/td>\n6.708<\/td>\n<\/tr>\n
      21<\/td>\n4.583<\/td>\n46<\/td>\n6.6.782<\/td>\n<\/tr>\n
      22<\/td>\n4.690<\/td>\n47<\/td>\n6.856<\/td>\n<\/tr>\n
      23<\/td>\n4.796<\/td>\n48<\/td>\n6.928<\/td>\n<\/tr>\n
      24<\/td>\n4.899<\/td>\n49<\/td>\n7<\/td>\n<\/tr>\n
      25<\/td>\n5<\/td>\n50<\/td>\n7.071<\/td>\n<\/tr>\n<\/thead>\n<\/table>\n

       <\/p>\n

      Solved examples<\/strong><\/h3>\n

      Question 1:<\/strong> What will the radius of a circle be if its area is given as\u00a0 625\u03c0 cm2<\/sup><\/p>\n

      Solution :<\/strong> Given, the area of the circle = 625\u03c0 cm2<\/sup><\/p>\n

      Now, area = \u03c0r2<\/sup><\/p>\n

      So,<\/p>\n

      \u03c0r2 <\/sup>= 625\u03c0 cm2<\/sup><\/p>\n

      We get, r2 <\/sup>= 625 cm2<\/sup><\/p>\n

      r = \u221a625 cm2<\/sup><\/p>\n

      Putting the value of \u221a625 in the above equation,<\/p>\n

      We get, r = 25 cm<\/p>\n

      Therefore, the radius of the circle is 25 cm.<\/p>\n

       <\/p>\n

      Question 2:<\/strong> Simplify \u221a81 + \u221a625 – \u221a144. (Note that all values of square roots will be positive)<\/p>\n

      Solution:<\/strong> Given, \u221a81 + \u221a625 – \u221a144<\/p>\n

      We know that \u221a81 = +9, \u221a144 = +12\u00a0 and \u221a625 = +25<\/p>\n

      Putting these square root values in the equation<\/p>\n

      We get, 9 + 25 – 12 = 22<\/p>\n

      So,\u00a0 \u221a81 + \u221a625 – \u221a144 upon simplification gives 22.<\/p>\n

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      Explore Other Topics<\/h1>\n

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      \n
      Geometry<\/a><\/div>\n
      Trigonometry<\/a><\/div>\n
      Operations<\/a><\/div>\n
      Numbers<\/a><\/div>\n<\/div>\n

      [\/et_pb_text][et_pb_text admin_label=”Related Concepts
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      Related Concepts<\/h1>\n

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      Square root of 100<\/a><\/div>\n
      Square root of 144<\/a><\/div>\n
      Square and Square roots<\/a><\/div>\n

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      Frequently Asked Questions<\/h1>\n

      1.<\/strong> What is the value of squares of all odd numbers between 1 and 25?<\/span>
      Ans:<\/strong> The values of squares of odd numbers between 1 and 25 are as follows:<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
      Odd numbers<\/b><\/td>\nSquare<\/b><\/td>\n<\/tr>\n
      3<\/span><\/td>\n9<\/span><\/td>\n<\/tr>\n
      5<\/span><\/td>\n25<\/span><\/td>\n<\/tr>\n
      7<\/span><\/td>\n49<\/span><\/td>\n<\/tr>\n
      9<\/span><\/td>\n81<\/span><\/td>\n<\/tr>\n
      11<\/span><\/td>\n121<\/span><\/td>\n<\/tr>\n
      13<\/span><\/td>\n169<\/span><\/td>\n<\/tr>\n
      15<\/span><\/td>\n225<\/span><\/td>\n<\/tr>\n
      17<\/span><\/td>\n289<\/span><\/td>\n<\/tr>\n
      19<\/span><\/td>\n361<\/span><\/td>\n<\/tr>\n
      21<\/span><\/td>\n441<\/span><\/td>\n<\/tr>\n
      23<\/span><\/td>\n529<\/span><\/td>\n<\/tr>\n
      25<\/span><\/td>\n625<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

       <\/p>\n

      2.<\/strong> What is the value of root 625?<\/span>
      Ans:<\/strong> The value of <\/span>\u221a625 is +25 and -25.<\/span><\/p>\n

      3.<\/strong> Is root 625 rational or irrational?<\/span>
      Ans<\/strong>: Root 625 is a rational number because the value of <\/span>\u221a625 is a whole number, i.e., 25.<\/span><\/p>\n

      [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

      The value of the square root of 625 is 25. It is a perfect square number. Read this article to know more about root 625.<\/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":"\nSquare root of 625 - Value and Derivation - mydomain<\/title>\n<meta name=\"description\" content=\"The value of the square root of 625 is 25. It is a perfect square number. 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