Question

For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square Mumber. Also find the square root of the square number, so obtained : (D 1100 (ii) 180 (11 735 (iv) 1008.,
btao please I beg.​

Answer 1

Answer:

Therefore, the number 6084 has 3 pairs of equal prime factors . Hence, the smallest number by which 2028 must be multiplied so that the product is a perfect square is 7. And the square root of the new number is √6084=78. Here, 3 are in pair, but 2 needs a pair to make 1458 a perfect square.

Answer 2

Answer:

180 = 2 x 2 x 3 x 3 x 5

Here, prime factor 5 has no pair. Therefore 180 must be multiplied by 5 to make it a perfect square.

\therefore180\times5=900

And \sqrt{900}=2\times3\times5=30

(iii) 1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7

Here, prime factor 7 has no pair. Therefore 1008 must be multiplied by 7 to make it a perfect square.

\therefore1008\times7=7056

And \sqrt{7056}=2\times2\times3\times7=84

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