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.
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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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Answered by
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
•••••
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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