# Square Root Formula

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Square root of a number or an expression is represented by a radical sign ‘√’ and the square root of a number means that the number is raised to an exponent of ‘1/2’. In order to find the square root of a number, we have to find the number which when multiplied by itself gives the given number. Perfect squares are the numbers which give a perfect number when taken their square root. The square root of a number which is not a perfect square can be calculated by simplification.

Example 1: What is the square root of 64?

Square root of ‘64’ can be also represented with the radical sign as ‘√64’.

In order to find its value, we need to find the numbers which when multiplied by itself gives ‘64’.

8 * 8 = 64 and we also have -8 * -8= 64.

This implies that 8 multiplied by itself or -8 multiplied by itself gives 64 as the answer and 64 is the perfect square.

Hence, square root of 64, which implies √64 = ±8.

Example 2: Simplify the square root of 48?

Here 48 is not a perfect square since there is no number which can multiply by itself to give 48.

So now prime factorization of 48 gives==> 48 = 2 * 2 * 2 * 2 * 3.

This implies: √48 = √(2 * 2 * 2 * 2 * 3)

Now we can pull out the numbers which are repeating twice inside==> 2 * 2 * √3.

Hence √48 = 4√3.

Therefore the simplified form of √48 = 4√3.