Question

For 6300 find the smallest whole number by which it should be divided so as to get a perfect square.Also find the square root of the square number so obtained​

Answer 1

First, we need to do prime factorization of 6300.

$\begin{array}{r | l} 2 & 6300 \\ \cline{2-2} 2 & 3150 \\ \cline{2-2} 5 & 1575 \\ \cline{2-2} 5 & 315 \\\cline{2-2} 3 & 63 \\ \cline{2-2} 3 & 21 \\\cline{2-2} & 7 \\\end{array}$

6300 ⇒ 2 × 2 × 5 × 5 × 3 × 3 × 7

Now we need to pair the numbers.

6300 ⇒ (2 × 2) × (5 × 5) × (3 × 3) × 7

Since 7 does not have a pair 6300 is not a perfect square.

∴ We need to divide 7 to get a perfect square.

6300 ÷ 7 = 900

Now we have to do prime factorization of 900

$\begin{array}{r | l} 2 & 900 \\ \cline{2-2} 2 & 450 \\ \cline{2-2} 5 & 225 \\ \cline{2-2} 5 & 45 \\ \cline{2-2} 3 & 9 \\ \cline{2-2} & 3 \\ \end{array}$

900 ⇒ 2 × 2 × 5 × 5 × 3 × 3

Now we need to pair them.

900 ⇒  (2 × 2) × (5 × 5) × (3 × 3)

To find the square root of 900 we need to take one number from each pair and multiply like this ⇒

√900 ⇒ 2 × 5 × 3

∴ √900 = 30