Question

2800 - 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

2800= 2×2×2×2×5×5×7
Pairs are= 2×2,2×2,5×5
Unpaired no. = 7
Divide 2800/7 = 400
√400= 20
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Answer 2

Solution :

Resolving 2800 into product of

prime , we get

2 | 2800
________
2 | 1400
________
2 | 700
________
2 | 350
________
5 | 175
________
5 | 35
________
*****7

2800 = 2×2×2×2×5×5×7

= ( 2×2 )×( 2 × 2 )×(5×5) × 7

We see that 2 , 2 , 5 exist in pairs ,

while 7 is alone.

So, we must divide given number

by 7 ,

Perfect square obtained = 2800/7

= 400

= ( 2 × 2 )× ( 2 × 2 ) × ( 5 × 5 )

The square root of 400

= √400

= √( 2 × 2 )( 2 × 2 )( 5 × 5 )

= 2 × 2 × 5

= 20

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