Question

find the square root of 5625 by prime factorization method​

Answer 1

Answer:

The prime factors of 5625 is 3 x 3 x 5 x 5 x 5 x 5. Hence, 3^2 x 5^2 x 5^2 = 5625. Thus the square root of 5625 is 75.

Answer 2

Given :  number 5625  

To find:  square root by prime factorization

Solution :

5625 =  3 *  1875

=> 5625 =  3 * 3 * 625

=> 5625 = 3 * 3 * 5 * 125

=> 56265 =  3 * 3 * 5 * 5 * 25

=> 5625 = 3 * 3 * 5 * 5 * 5 * 5

=> 5625 = 3² * 5² * 5²

=> 5625 = ( 3* 5 * 5)²

=> 5625 = 75²

√5625 = √ 75²

=> √5625 = 75

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