# Solving Square Roots

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Square root is the number which when multiplied by itself gives back the number to which square root is calculated. Square root is one of the commonly used terms in numerical calculations and algebra. Principal square root is the nonnegative root of the given nonnegative real number. There is no principle square root of a negative number because the principal square root cannot be applied to imaginary number. The symbol of square root is √.

Example 1: Find the square root of the number 225x2?

Solution: Given here is to find the principal square root of the number 225.

The square root of 225 is the number when multiplied to itself gives back 225.

So, √225x2 = √ (3* 3* 5* 5*x*x) = √ (15x * 15x) = 15x or -15x.

But we need to find the principal square root of the number 225 which has to be a positive value.

Hence, the principal square root of 225 is 15x.

Example 2: Find the square root of the number 400?

Solution: Given here is to find the principal square root of the number 400.

The square root of 400 is the number when multiplied to itself gives back 400.

So, √400 = √ (2* 2 *5* 5* 2* 2) = √ (4 * 4* 5* 5) = √ (20* 20) = 20 or -20.

But we need to find the principal square root of the number 200 which has to be a positive value.

Hence, the principal square root of 400 is 20.