Square Root of 56

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Square root of 56 is calculated by splitting 56 into its prime factors and hence 56 can be written as 2 * 2 * 2 * 7. So, the square root of 56 is equal to √(2 * 2 * 2 * 7). Now in order to simplify the square root, we can pull out the numbers which are repeatedly multiplied twice. This gives 2 * √(2 * 7) = 2 * √14 = 2√14. Therefore the square root of 56 is given as √56 = 2√14.

Example 1: Simplify the given expression, √4 * √56.

Here each square root radical should be simplified further.

√4 = √(2 * 2). Now pull out the number which is repeating twice inside the radical.

This gives: √4 = 2and ‘4’ is a perfect square since its square root gives a perfect number!

And we already have 56 = 2√14.

So, √4 * √56 = 2 * 2√14 = 4√14.

Hence the value of the expression, √4 * √56is = 4√14.
 
Example 2: Simplify the given expression, √14 + √56.

Here each square root radical should be simplified further.

√14 = √(2 * 7) and it is already in its simplified form as no number is repeating twice inside the radical to be pulled out.

And we have 56 = 2√14.

So, √14 + √56 = 1√14 +2√14 = (1 + 2) √14 = 3√14.

(They are like terms since they have the same radical √14 and hence can be added).

Hence the value of the expression, √14 + √56 is = 3√14.
 
 
 

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