Square Root of 75

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Square root of 75 can be calculated using the prime factorization method. Square root of 75 is represented as √75 where ‘√’ is the square root radical sign. In order to find the square root of 75, we can first split the number 75 into its prime factors which implies 75 = 3 * 5 * 5. Hence we get √75 = √(3 * 5 * 5) and now we can simplify this further by pulling out the number repeating twice inside the radical. Therefore we get, √75 = 5√3.
 
Example 1: Simplify the given expression, √3 + √75.

Here each square root radical should be simplified further.

√3 cannot be simplified further as it is already in its simplified form since no number is repeating twice inside the radical to be pulled out.

And we have 75 = 5√3.

So, √3 + √75 = 1√3 + 5√3 = (1 + 5) √3 = 6√3.

(They are like terms since they have the same radical √3 and hence can be added).

Hence the value of the expression, √3 + √75 is = 6√3.
 
Example 2: Simplify the given expression, √3 * √75.

Here each square root radical should be simplified further.

√3 cannot be simplified further as it is already in its simplified form since no number is repeating twice inside the radical to be pulled out.

And we have 75 = 5√3.

So, √3 * √75 = √3 * 5√3 = 5 * √(3 * 3) = 5 * 3= 15.

Hence the value of the expression, √3 *√75 is = 15.
 
 
 

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