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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