Gujarat BoardEnglish MediumSTD 8MATHSCubes and Cube Roots2 Marks
Question
Evaluate: $\sqrt[3]{700\times2\times49\times5}$
✓
Answer
Property: For any two integers a and b, $\sqrt[3]{\text{ab}}=\sqrt[3]{\text{a}}\times\sqrt[3]{\text{b}},$ From the above property, we have: $\sqrt[3]{700\times2\times49\times5}$
$=\sqrt[3]{2\times2\times5\times5\times7\times2\times7\times7\times5}$
$\therefore$ $700 = 2 \times 2 \times 5 \times 5 \times 7$ and $49 = 7 \times 7$ $=\sqrt[3]{2^3\times5^3\times7^3}$
$=\sqrt[3]{2^3}\times\sqrt[3]5^3\times\sqrt[3]{7^3}$
$=2\times5\times7=70$
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