Question

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IMAGE ATTACHED ANSEWER




For each of the following numbers, find the smallest whole number by which it should
be multiplied so as to get a perfect square number. Also find the square root of the
square number so obtained
252
180
1008
2028
1458
768​

Answer 1

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(i) 252

Answer: By prime factorisation we get,

252 = 2 x 2 x 3 x 3 x 7

Here, 2 and 3 are in pairs but 7 needs a pair. Thus, 7 can become pair after multiplying 252 with 7.

So, 252 will become a perfect square when multiplied by 7.

Thus, Answer = 7

(ii) 180

Answer: By prime factorisation, we get, 180 = 3 x 3 x 2 x 2 x 5

Here, 3 and 2 are in pair but 5 needs a pair to make 180 a perfect square.

180 needs to be multiplied by 5 to become a perfect square.

Thus, Answer = 5

(iii) 1008

Answer: By prime factorisation of 1008, we get

1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7

Here, 2 and 3 are in pair, but 7 needs a pair to make 1008 a perfect square.

Thus, 1008 needs to be multiplied by 7 to become a perfect square

Hence, Answer = 7

(iv) 2028

Answer: By prime factorisation of 2028, we get

2028 = 2 x 2 x 3 x 13 x 13

Here, 2 and 13 are in pair, but 3 needs a pair to make 2028 a perfect square.

Thus, 2028 needs to be multiplied by 3 to become a perfect square.

Hence, Answer = 3

(v) 1458

Answer: By prime factorisation of 1458, we get

1458 = 2 x 3 x 3 x 3 x 3 x 3 x 3

Here, 3 are in pair, but 2 needs a pair to make 1458 a perfect square.

So, 1458 needs to be multiplied by 2 to become a perfect square.

Therefore, Answer = 2

(vi) 768

Answer: By prime factorisation of 768, we get

768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

Here, 2 are in pair, but 3 needs a pair to make 768 a perfect square.

So, 768 needs to be multiplied by 3 to become a perfect square.

Hence, Answer = 3

Answer 2

SOLUTION

Refer to the attachment

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