Question

Which is the smallest number that can be multiplied with the given number to get a perfect square?
(1) 7
(2) 75

Answer 1

(1) do the prime factorization of 7, i.e.,
7
now to make 7 as perfect square we have to multiply it with 7
7×7= 49
and square root of 49 is 7

(2) do the prime factorization of 75,i.e.,
3×5×5
now make the pairs
1st pair - 5×5
therefore to make 75 as perfect square we have to multiply it by 3
75×3=225
and square root of 225 is 15


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Answer 2

i ) 7 should be multiplied

with 7 to get a perfect square

7 × 7 = 7²

ii ) Smallest number multiplied

to get perfect square of 75 is 3

Since ,

75 = 3 × 5²

If we multiply with 3 , we get

3 × 75 = 3 × 3 × 5 × 5

= 3² × 5²

= ( 3 × 5 )²

= 15² ( PERFECT SQUARE )

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