Question

Find the square root of 5929 by the prime factorization method.

Answer 1

Hint-prime factorization means splitting the number into multiplication of certain prime numbers. Square root of a number $x$ is that number $y$ which is multiplied twice to get back $x$ i.e. ${y^2} = x,{\text{ y is a square root of x}}$.

Complete step-by-step answer:
5929 can be broken into prime factors
5929 = $7 \times 7 \times 11 \times 11$
$
   \Rightarrow \sqrt {5929} = \sqrt {7 \times 7 \times 11 \times 11} \\
   = \sqrt {{7^2} \times {{11}^2}} \\
   = 7 \times 11 \\
   = 77 \\
$
Therefore, the square root of 5929 is 77.

Note-Whenever we come across this type of question try to find the prime factors of the given number and in square root try to get the prime numbers in pairs. The paired number comes out of the square root.