Question

. For each of the following numbers, find the smallest whole number by which it shoul be divided so as to get a perfect square. Also find the square root of the squa number so obtained. (i) 252 (ii) 2925 (ii) 396 (iv) 2645 (v) 2800 (vi) 1620 ​

Answer 1

Question:-

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

Solution:

(i) 252 = 2 x 2 x 3 x 3 x 7

Here, prime factor 7 has no pair. Therefore 252 must be divided by 7 to make it a perfect square.

\therefore252\div7=36

And \sqrt{36}=2\times3=6

(ii) 2925 = 3 x 3 x 5 x 5 x 13

Here, prime factor 13 has no pair. Therefore 2925 must be divided by 13 to make it a perfect square.

\therefore2925\div13=225

And \sqrt{225}=3\times5=15

(iii) 396 = 2 x 2 x 3 x 3 x 11

Here, prime factor 11 has no pair. Therefore 396 must be divided by 11 to make it a perfect square.

\therefore396\div11=36

And \sqrt{36}=2\times3=6

(iv) 2645 = 5 x 23 x 23

Here, prime factor 5 has no pair. Therefore 2645 must be divided by 5 to make it a perfect square.

\therefore2645\div5=529

And \sqrt{529}=23

(v) 2800 = 2 x 2 x 2 x 2 x 5 x 5 x 7

Here, prime factor 7 has no pair. Therefore 2800 must be divided by 7 to make it a perfect square.

\therefore2800\div7=400

And \sqrt{400}=2\times2\times5=20

(vi) 1620 = 2 x 2 x 3 x 3 x 3 x 3 x 5

Here, prime factor 5 has no pair. Therefore 1620 must be divided by 5 to make it a perfect square.

\therefore1620\div5=324

And \sqrt{324}=2\times3\times3=18

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