Question

: Find the smallest whole number by which $2925$ should be multiplied so as to get a perfect square number. Also find its square root.

Answer 1

Hint: First we will do prime factorization of $2925$. Thereafter we will make a pair of prime factors. Further we will multiply $2925$by that factor is not in pairing. After the multiply $2925$ to get the answer. By using formula: Square root by prime factorization method


Complete step by step solution:
Given number $2925$ which is add number.

3	2925
3	975
5	65
5	65
13	13
	1

$2925 = \overline {3 \times 3} \times \overline {5 \times 5} \times 13$ .
Here, prime factor $13$ has no pair. Therefore $2925$ must be multiplied by $13$ to make it a perfect square.
$\therefore \,2925 \times 13 = 38,025$
So $\sqrt {38025} = \sqrt {\overline {3 \times 3} \times \overline {5 \times 5} \times \overline {13 \times 13} } $
$ = 3 \times 5 \times 13 = 195$
Hence square root of $\sqrt {38025} = 195$


Note: In this type of question we find the smallest whole number then we calculate the square root of the number. In the prime factorization ,we will multiply by that number which is not in pairs.