Q.6 For each of the following numbers, 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.

(i) 252

(ii) 2925

(iii) 396

(iv) 2645

(v) 2800

(vi) 1620

Answers (1)

D Devendra Khairwa

(i) 252: Prime factorization of 252 gives = $2\times2\times3\times3\times7$ .

For making pairs we will divide the given number by 7.

The obtained number is 36 and its square root is 6.

(ii) 2925: Prime factorization of 2925 gives = $3\times3\times5\times5\times13$

To make pairs divide the given number by 13.

So the obtained number is 225 and its square root is 15.

(iii) 396: Prime factorization if 396 = $2\times2\times3\times3\times11$

For obtaining perfect square number we need to divide the given number by 11.

So the required number is 36 and its square root is 6.

(iv) 2645: Prime factorization of 2645 = $5\times23\times23$

We need to divide the given number by 5 to obtain the perfect square number.

So the obtained number is 529 and its square root is 23.

(v) 2800: Prime factorization of 2800 = $2\times2\times2\times2\times5\times5\times7$

To make pairs we need to divide 2800 by 7.

So the required number is 400 and its square root is 20.

(vi) 1620: Prime factorization of 1620 gives = $2\times2\times3\times3\times3\times3\times5$

To make pairs divide the given number by 5.

We get , number = 324 and its square root = 18.