Square Root calculator with steps

Square Root calculator

Square root of a number is the inverse operation of squaring number. In simple terms, square root of a number is a factor’s number when multiplied by itself it gives the original number. When you multiply a number by itself, you find the square. Square and square roots are unique exponents. In addition to that, square of a number is always a positive number. For this reason, any number has two square root, where one is a positive value while the other is a negative value. For instance, 3 and -3 are square roots of 9. 2 and -2 are the square roots of 4.

Square root formula

Square root formula helps to find the square root of a number. The exponent formula is (-). You can use many methods to find square root, this include prime factorization, long division etc.

How to find square root

There are four methods to find square root of a number. They include:

        Repeated Subtraction Method of Square Root.

        Prime Factorization method.

        Square Root by Estimation Method.

Repeated Subtraction Method of Square Root

This simple method involves subtracting the “consecutive odd numbers” from the given number for finding the square root until 0. The square root of the number is the number of times we subtract. Moreover, this method works for perfect squares. Here is an example of finding square root using this method:

Example: Find The Square root of 36 using repeated subtraction method

36- 1 =35

35- 3 = 32

32- 5 = 27

27- 7 = 20

20 – 9 = 11

11 – 11 = 0

The square root of 36 is 6 since we have subtracted 36 by odd numbers 6 times

Prime factorization Method

Prime factorization involves representing a given number as a product of prime numbers. The following steps help to find square root of a number through prime factorization method:

        Divide the number into its prime factors.

        Create pairs of same factors to have equal pair of factors.

        Pick one factor from the pair.

        Calculate the product of the factors got by picking one factor from each pair.

        The product is the square root of that number.

Let’s find out square root using prime factorization method:

Example: Find the Square Root of 81 using Prime Factorization Method

The prime factors are

3 x 3 x 3 x 3

Arrange in similar pairs

(3 x 3) (3 x 3)

Pick one number in each pair and find its product

3 x 3 = 9

Therefore the square root of 81 is 9


Square root video tutorial