Let $x$ and $y$ be natural numbers. If $x$ divides $y$ , then $x^{3}$ divides $y^{3}$ . State whether the statement is true or false.

True

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False

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Solution

The correct option is A True
Prove the statement:
Natural numbers = $\{1, 2, 3, . . . . .\}$
Given: $x$ and $y$ are natural numbers and $x$ divides $y$ .
Therefore, $\frac{y}{x}$ is a natural number.
Now, $\frac{y^{3}}{x^{3}}$ can be written as ${(\frac{y}{x})}^{3}$ .
Since the cube of a natural number is also a natural number.
Hence, $x^{3}$ divides $y^{3}$ .
Hence,the given statement is true.

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