Square Roots

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Square root is a function which is represented with the symbol ‘√’, and a number or an expression can be placed inside the square root radical. Square root of a number or an expression indicates that the exponent on that number or the expression is ‘1/2’. This implies that the square root radical represents the exponent of 1/2. The expression or number inside the square root radical should be greater than or equal to 0, and if it’s less than 0, then the solution is not real but it is called an imaginary solution.

Example 1: What is the value of ‘x’ if √625 = x?

Here the given square root number should be simplified furtherby splitting the number into its prime factors, in order to get the value of ‘x’

√625 = √(5 * 5 * 5 * 5). Now pull out the number which is repeating twice inside the radical.

This gives: 625 = 5 * 5 = 25.

So, √625 = x and this implies 25 = x.

Therefore the value of ‘x’ in the given square root equation is 25.
 
Example 2: What is the value of ‘x’ if √729 = x?

The given number should be split into its prime factors to get the value of x.

√729 = √(3 * 3 * 3 * 3 * 3 * 3). Now pull out the number which is repeating twice inside the radical.

This gives: 729 = 3 * 3 * 3 = 27

So, √729= x and this implies 27 = x.

Therefore the value of ‘x’ in the given square root equation is 27.
 
 
 

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