Question

by what is smallest must 180 be multiplied their it become a perfect square also find the square root of the perfect square so obtained​

Answer 1

Hey Mate here is your answer:-

Number-180

We must factorise the 180 to get the requierd number

So,

2|180

2|90

5|45

9|5

5|5

1

Pairs formed- 2×2×5×5×9

So 9 is the requiered number.

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Answer 2

Given Number - 180.

By prime factorisation 180 , we get ,

180 = 2 × 90.

= 2 × 2 × 45.

= 2 × 2 × 5 × 9.

= 2 × 2 × 5 × 3 × 3.

= [tex]2^{2}[/tex] × 5 × [tex]3{^2}[/tex]

So, it is clear that the number should be multiplied by 5 to make a perfect square.

Therefore , required no. = 4 × 5 × 5 × 9 = 900.

And √900 is a square of 30>