Question

Find the smallest number by which 2925 must be divided to obtain a perfect square. Also find the square root of the perfect square so obtained:-

Answer 1

Answer:

2925 = 3 × 3 × 5 × 5 × 13

Hence, 13 is the smallest number by which 2925 must be divided to obtain a perfect square.

2925 ÷ 13 = 225

Square root = √225 = 15

Answer 2

AnsWer :

13 is the smallest number by which 2925 must be divided to obtain a perfect square.

Solution :

We have, Number be 2,925.

• N1 = 2, 925.

Prime factorization.

$\begin{array}{r | l} 3 & 2925 \\ \cline{2-2} 3 & 975 \\ \cline{2-2} 5 & 325 \\ \cline{2-2} 5 & 65 \\ \cline{2-2} 13 & 13 \\ \cline{2-2} & 1 \end{array}$

We can Express 2,925.

$\tt\bigstar \: 2925\leadsto 3 \times 3 \times 5 \times 5 \times 13.$

Note : When we Divided both sides by 13, We get perfect Square.

$\rule{90}1$

$\tt \mapsto \dfrac{ 2925}{13} = \dfrac{ 3 \times 3 \times 5 \times 5 \times 13}{13}$

$\tt \mapsto 225 = 3 \times 3 \times 5 \times 5.$

$\rule{90}1$

Now,

Roots of 225.

$\tt \mapsto \sqrt{225}$

$\tt \mapsto 15.$

Therefore, the smallest number Which divided to get perfect root be 13.