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Finding Square Roots.

Square root

When a number is multiplied by itself it gives another number known as the square root of that number. For example, if we divide 2 by 2 so the number we get is 4, it means the square root of 2 is 4. We can write it in two different forms, 2 × 2 or 2^2. The term that refers to square root of the number is 1/2, 1/2 = √. It means √n = n^1/2.

Square root is a number whose product by itself gives the original number. It is denoted by the sign known as Radical (√), while the number under it is known as Radicand.

Finding Square Root

It is not a big task to find a square root of a particular number, we just have to find a perfect square of the number. For example, if we want to find the square root of 36, then we have to find a number whose product is 36 by dividing it by himself, which is 6. It can be represented as √36 = √6^2 = 6. There are four major methods to find the square root of a number, as follows:

  • Repeated Subtraction Method

  • Prime Factorization method

  • Estimation method

  • Long Division Method

Repeated Subtraction Method

In this method we subtract odd numbers until the result is zero from the number whose square root is to be founded. The number of times subtraction is done is known as the square root of that number. This technique only works in perfect squares. Let's find the square root of 9.

9 - 1 = 8

8 - 3 = 5

5 - 5 = 0

As the subtraction is done 3 times therefore the answer is; √9 = 3.

Prime Factorization Method

Representing a number by the product of the prime numbers is known as the Prime Factorization method. To find the square root of a particular number through this technique we have to go through the following steps.

  1. Divide the numbers into it's prime factors.

  2. Form pairs of equal factors.

  3. Take one factor from the pair.

  4. Find the product.

  5. The product is the square root of the given number.

Below is the example:


Square Root Table

Square root table

Square root formula

Exponent formula = √x = x^1/n

Square root and finding a perfect square is broader topic, it includes information like simplifying squares, square root of a negative number and square of a number etc.


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