Gujarat BoardEnglish MediumSTD 8MATHSCubes and Cube Roots1 Mark
Question
If a divides b, then a3 divides b3.
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Answer
True. Solution: $\because$ a divides b $\therefore\frac{\text{b}^3}{\text{a}^3}=\frac{\text{b}\times\text{b}\times\text{b}}{\text{a}\times\text{a}\times\text{a}}=\frac{\text{(ak)}\times\text{(ak)}\times\text{(ak)}}{\text{a}\times\text{a}\times\text{a}}$ $\because$ a divides b $\therefore$ b = ak fore some k $\therefore\frac{\text{b}^3}{\text{a}^3}=\frac{\text{(ak)}\times\text{(ak)}\times\text{(ak)}}{\text{a}\times\text{a}\times\text{a}}=\text{k}^3$ $\Rightarrow\text{k}^3=\text{b}^3=\text{a}^3(\text{k}^3)$ $\therefore$ a3 divides b3
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