Value of Root 5

Value of root 5 could be evaluated, by long division method, as we know 5 is not a perfect square. Basically, the square root or root of a number “n”  is a number that gives the number “n” when multiplied by itself. For example, the value of root 9 is 3 as, 3 x 3 = 9, because 9 is the perfect square.

When we multiply any number to itself, we get the square of that number. Evaluation or calculation of the square root of the perfect square number is easier than the non-perfect square numbers. To find the square root of a number, we have to inverse the process of squaring the number, which is the formula to find it. In this section, will see how to find the value of root 5.

Examples of perfect square:-

4 = square of a number 2 = 2 × 2 = 22

36 = square of a number 6 = 6 × 6 = 62

49 = square of a number 7 = 7 × 7 = 72

121 = square of a number 11 = 11 × 11 = 112

You can also find some of the examples for perfect square numbers in the square root table. It’s difficult to find the square root value for the non-perfect square numbers i.e., 3, 5, 7, 10 etc., in general. Therefore, we use a classic method is available to find the value of root 5. This method is also called a Long division method.

The symbol used to denote the square root is ‘√’. The square root symbol is also known as a radical symbol or radix. The number underneath the radical symbol is called as radicand. If the given number is not a square number, then the value should take either radical form or decimal form.

Division Method to Find the Value of Root 5

It is possible to find the value of roots of any number, by the help of the long division method. The steps for finding the value of root 5 is given below:

Step 1: The number 5 can be written as 5.00000000. i.e., 5 = 5.00 00 00 00

Step 2: Take the number whose square is below 5. So, 4 is the perfect square of number 2 and is below 5.

Step 3: Write the number 2 in both divisor and quotient place, such that when 2 multiplied by 2 gives 4. Subtract 4 from 5, you will get the answer 1.

Step 4: Next carry down two zeros and write down after 1 and take the decimal point after 1 in the quotient.

Step 5: Now add 2 in divisor to make it 4. Take a number next to 4, such that when we multiply the combination with the same number, we get a number which is less than or equal to 100. Hence, we will take here 2, such that 42 multiplied by 2 gives 84, which is less than 100. Subtract it with 100 now to get the remainder. So, the remainder is 16.

Step 6: Now again write down two zero’s and repeat step 5 up to 4 places of decimals.

Step 7: Finally, you get the quotient value as 2.2360, which is approximately equal to 1.236.

How to Find Root 5

Check below the step-by-step procedure of long division method to find the square root of 5.

Value of root 5

Therefore, the value of root 5 is,

√5 = 2.2360…


√5 ≈ 2.24

You can find the value of the square root of all the non-perfect square number with the help of the long division method. This is the old method which gives the exact value of the root of numbers. To get more knowledge on roots of numbers and other Maths related topics, stay tuned with BYJU’S.

Also Check: Value of root 3

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Related Links
Square Root Table Square Root Calculator
Square Root Of 5 Square Root Formula


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  1. I still can’t understand please give each and every step. It’s a request.

  2. Explanation is very clear