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  4. Find the sequential order of steps to find the square root of n by prime factorization method. (A) The product of the primes is the square root of n. (B) Divide n into the prime factors. (C) Pair the similar factors such that factors in each pair are equal. (D) Take out one prime from each pair.

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Q. Find the sequential order of steps to find the square root of $n$ by prime factorization method.
(A) The product of the primes is the square root of $n$.
(B) Divide $n$ into the prime factors.
(C) Pair the similar factors such that factors in each pair are equal.
(D) Take out one prime from each pair.

Squares and Square Roots and Cubes and Cube Roots

Solution:

Suppose $n=16$
At first we find out the prime factor of 16
$16=2 \times 2 \times 2 \times 2$....(B)
Now, making pairs
$2 \times 2,2 \times 2$....(C)
Choose one factor from the pairs will be $2 \times 2=4$...(D)
Hence, square root of 16 will be 4 ....(A)