Find the two-digit number which a square number is and also a cubic number.

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.