8. For each of the following numbers, find the smallest number by which we divide it so
as to get a perfect square. Also find the square root of the square numbers so
obtained.
a. 37845
b. 2800
C. 45056
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2800=2×2×2×2×5×5
Since the prime factor 7 does not in pairs.
Therefore,2800 is not a perfect square.
The smallest number by which 2800 must be divided to obtain a perfect square=7
Therefore cubic no.=2800÷7 = 400
square root =(2×2)×(2×2)×(5×5)
=2×2×5
=20(ans)
45056=2×2×2×2×2×2×2×2×2×2×2×2×11
Since the prime factor 11 does not occur in pairs.
therefore, 45056 is not a perfect square.
The smallest number by which 45056 must be divided to obtain a perfect square =11
therefore cubic no.=45056÷11 = 44096
square root=(2×2)×(2×2)×(2×2)×(2×2)×(2×2)×(2×2)
=2×2×2×2×2×2
=64 (ans)
Hope this will help you
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=2×2×2×2×2×2
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