QUESTION

# Find the square root of a number 5929 by Prime Factorisation Method.

Hint: In this question the prime factorisation of a number is the determination of the set of prime integers which multiply together to give the original integer. To solve the above question, write the prime factors of 5929 which are 7, 7, 11, 11 and then proceed step by step to solve.

We need to determine the set of prime integers which when multiplied together gives the original number.
Dividing the given number, i.e., 5929 by the prime factor 7, we will get-
$5929 \div 7 = 847 \to (1)$
Now dividing the result, we get in equation (1) by the prime factor 7, we get-
$847 \div 7 = 121$
Similarly, dividing 121 by the prime factor 11, we get-
$121 \div 11 = 11$
Now, dividing 11 by the prime factor 11, we get-
$11 \div 11 = 1$
So, the Prime Factors of 5929 are 7, 7, 11, 11.
Therefore, $5929 = 7 \times 7 \times 11 \times 11$
We took the pairs of 7 and 11.
Hence, the square root of $5929 = 7 \times 11 = 77$.
Therefore, the square root of 5929 found by Prime Factorisation Method is 77.

Note: Whenever such type of questions appears, then first find the prime factors of the given number, then write the number in terms of its prime factors as, $5929 = 7 \times 7 \times 11 \times 11$, take the pairs of 7 and 11, multiplying 7 and 11 we get the square root of the given number, 5929.