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 = x^{2}

⇒ A number which is a cube must equal to = y^{3}

⇒ Number must be sixth power of an integer = z^{6}

∴ we can have x = z^{3} and y = z^{2} so x^{2} = z^{6} and y^{3} = z^{6}

By trial and error method 1^{6} = 1 , 2^{6} = 64 and 3^{6} = 729 (need two digit number).

So, 64 is the number.

⇒ 8^{2} = 64 = 4^{3}

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

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