 ## Book: NCERT - Mathematics

### Chapter: 6. Squares and Square Roots

#### Subject: Maths - Class 8th

##### Q. No. 6 of Exercises 6.3

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

(i) 252 can be factorized as follows:

252 = 2 * 2 * 3 * 3 * 7

Here, prime factor 7 does not have its pair

If we divide this number by 7, then the number will become a perfect square.

Therefore, 252 has to be divided by 7 to obtain a perfect square is a perfect square

36 = 2 * 2 * 3 * 3 = 6

(ii) The prime factorization of 2925 is as follows:

2925 = 3 * 3 * 5 * 5 * 13

Here, prime factor 13 does not have its pair

If we divide this number by 13, then the number will become a perfect square.

Therefore, 2925 has to be divided by 13 to obtain a perfect square is a perfect square

225 = 3 * 3 * 5 * 5 = 15

(iii) The prime factorization of 396 is as follows:

396 = 2 * 2 * 3 * 3 * 11

Here, prime factor 11 does not have its pair

If we divide this number by 11, then the number will become a perfect square.

Therefore, 396 has to be divided by 11 to obtain a perfect square is a perfect square

36 = 2 * 2 * 3 * 3 = 6

(iv) The prime factorization of 2645 is as follows:

2645 = 5 * 23 * 23

Here, prime factor 5 does not have its pair

If we divide this number by 5, then the number will become a perfect square. Therefore, 2645 has to be divided by 5 to obtain a perfect square is a perfect square

529 = 23 * 23 = 23

(v) 2800 can be factorized as follows:

2800 = 2 * 2 * 7 * 10 * 10

Here, prime factor 7 does not have its pair

If we divide this number by 7, then the number will become a perfect square. Therefore, 2800 has to be divided by 7 to obtain a perfect square is a perfect square

400 = 2 * 2 * 2 * 2 * 5 * 5 = 2 * 2 * 5

= 20

(vi) The prime factorization of 1620 is as follows:

1680 = 2 * 2 * 3 * 3 * 3 * 3 * 5

Here, prime factor 5 does not have its pair

If we divide this number by 5, then the number will become a perfect square.

Therefore, 1680 has to be divided by 5 to obtain a perfect square is a perfect square

324 = 2 * 2 * 3 * 3 * 3 * 3 = 18

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