Question

Find the square root the following by prime factorization.  

 7056

Answer 1

Resolving 7056 into prime factors:
7056 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 7 

Grouping the factors into pairs of equal factors:
7056 = (2 x 2) x (2 x 2) x (3 x 3) x (7 x 7)
Taking one factor for each pair, we get the square root of 705:
2 x 2 x 3 x 7 = 84