Square Root Simplifier

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Square root simplifier is the method in which the number inside the square root radical, represented by the symbol ‘√’ is simplified into its lowest numbers. A number inside a square root can be simplified further when the number is split into its prime factors. This is called prime factorization of a number and by factoring, a square root number can be written in its simplest form. Square root simplification makes a question easier and it also makes it easy for any other calculations.

Example 1: Simplify the given square root expression, √125 - √45.

Here each square root number should be simplified further.

√125 = √(5 * 5 * 5). Now pull out the number which is repeating twice inside the radical.

This gives: 125 = 5 * √5 = 5√5.

Similarly, 45 = √(3 * 3 * 5) = 3 * √5 = 3√5.

So, √125 - √45 = 5√5- 3√5 = 2√5.

(Since both have the same radical √5, they can be subtracted together!)

Hence the value of the expression √125 - √45 = 2√5.
 
Example 2: Simplify the given square root expression, √20 + √45.

Here each square root number should be simplified further.

√20 = √(2 * 2 * 5). Now pull out the number which is repeating twice inside the radical.

This gives: 20 = 2 * √5 = 2√5.

Similarly, √45 = √(3 * 3 * 5) = 3 * √5 = 3√5.

So, √20 + √45 = 2√5 + 3√5 = 5√5.

(Since both have the same radical √5, they can be added together!)

Hence the value of the expression √20+ √45 = 5√5.
 
 
 

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