Maharashtra BoardEnglish MediumSTD 9MathsRationalisation2 Marks
Question
Simplify the following:$\sqrt[3]{4}\times\sqrt[3]{16}$
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Answer
We know that $\sqrt[\text{n}]{\text{a}}\times\sqrt[\text{n}]{\text{b}}=\sqrt[\text{n}]{\text{ab}}.$ We will use this property to simplify the expression $\sqrt[3]{4}\times\sqrt[3]{16.}$$\therefore\ \sqrt[3]{4}\times\sqrt[3]{16.}=\sqrt[3]{64}$
$=\sqrt[3]{4^3}$
$=(4^3)^\frac{1}{3}$
$=(4)^1$
$=4$
Hence the value of the given expression is 4.
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