Question

180 - By which smallest number the given number should be multiplied,so that the result becomes a perfect square ? Find the square root of the result obtained.

Answer 1

Hello !


180 = 2 × 2 × 3 × 3 × 5

5 is unpaired ao we need to multiply it by 5
to make it a perfect square


180 × 5 = 900

and

$\sqrt{900} = 30$
Hope it helps

Answer 2

Solution :

Resolving 180 into product of prime,

we get

2 | 180
______
2 | 90
______
3 | 45
______
3 | 15
______
******5

180 = 2 × 2 × 3 × 3 × 5

= ( 2 × 2 ) × ( 3 × 3 ) × 5

We observe that 2 , 3 exists in pairs,

while 5 is alone .

So , we should multiply the given

number by 5 to get a perfect square.

Therefore ,

the perfect square so obtained is

180 × 5 = 900

= ( 30 )²

The square root of 900

= √900

= √(2×2)(3×3)(5×5)

= 2 × 3 × 5

= 30

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