Question

1620 - By which smallest number the given number should be divided, so that the result becomes a perfect square? Find the square root of the result obtained.

Answer 1

we must divided bye 5 to make it a perfect square and the square root of that number will be 18

Answer 2

Solution :

Resolving 1620 into product of prime,

we get

2 | 1620
_______
2 | 810
_______
3 | 405
_______
3 | 135
_______
3 | 45
_______
3 | 15
_______
*****5

Now ,

1620 = 2×2×3×3×3×3×5

= (2×2)×(3×3)×(3×3)×5

We see that 2 , 3 , 3 exists in pairs,

while 5 is alone .

So , we should divide the given

number by 5 .

Therefore , perfect square obtained

= 1620 ÷ 5

= 324

= ( 18 )²

The square root of 324 is

√324

= √( 2×2) × ( 3 × 3 ) × ( 3 × 3 )

= 2 × 3 × 3

= 18

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