Question

Find the square root of 5929.

Answer 1

Hint: Find the prime factors of 5929 the by prime factorization method find the square root of the given number.

Complete step-by-step answer:
We need to determine the set of prime integers which when multiplied together gives the original number.
So, the Prime Factors of 5929 are 7, 7, 11, 11.
Now, dividing the given number, i.e., 5929 by the prime factor 7, we will get-
 Dividing by 7 we get, $5929 \div 7 = 847 \to (1)$
Now dividing the result, we get in equation (1) by the 2nd prime factor, we get-
$847 \div 7 = 121$
Similarly, dividing 121 by 3rd prime factor i.e., 11, we get-
$121 \div 11 = 11$
Now, dividing 11 by the 4th prime factor i.e., 11, we get-
$11 \div 11 = 1$
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 a type of question 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.