Question

Find the square root of a number 729 by prime factorization method.

Answer 1

Hint: In order to solve this problem you have to factorize the number 729 by prime numbers and then make pairs of two to get the answer to this problem.
We need to find the square root of number 729 by prime factorization method.
Complete step-by-step solution:
So, the number 729 can be written as:
729 = 3 x 3 x 3 x 3 x 3 x 3
So square root of 729 can be written as $\sqrt {729} = \sqrt {3 \times 3 \times 3 \times 3 \times 3 \times 3} = \sqrt {{3^2} \times {3^2} \times {3^2}} = 3 \times 3 \times 3 = 27$
Hence the answer to this problem is 27.

Note: In this problem you have to factorize 729 in such a way that every factor in it is a prime number in pairs of two then you have to take the square root of it to get the answer to this problem. Proceeding like this you will get the right answer.