Q. 44.7( 17 Votes )

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Answer :

Need to find out a two-digit number which is a square number and also a cubic number.

A number which is a square must equal to = x2

A number which is a cube must equal to = y3

Number must be sixth power of an integer = z6

we can have x = z3 and y = z2 so x2 = z6 and y3 = z6

By trial and error method 16 = 1 , 26 = 64 and 36 = 729 (need two digit number).

So, 64 is the number.

82 = 64 = 43

Hence, 64 is the two-digit number which is a square number and also cubic number.

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