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It is not always true. For example, let m = -1 We have m 2 = (-1) 2 = 1 and m 3 = (-1) 3 = -1 ∴ The above statement, i.e. m 2 < m 3 is false.

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Cubes and Cube Roots

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Long Answer Type

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Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube. (i) 81 (ii) 128 (iii) 135 (iv) 192 (v) 704

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Short Answer Type

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16. State true or false: for any integer m, m² < m³. Why?

It is not always true.
For example, let m = -1
We have m²= (-1)²= 1
and m³= (-1)³= -1
∴ The above statement, i.e. m² < m³ is false.

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18.

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