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If $\sqrt{\sqrt[3]{x\times0.000009}}=0.3$, the find the value of $\sqrt{x}$.
Given: $\sqrt{\sqrt[3]{x\times0.000009}}=0.3$.
To do: To find the value of $\sqrt{x}$.
Solution:
As given, $\sqrt{\sqrt[3]{x\times0.000009}}=0.3$
$\Rightarrow ( \sqrt{\sqrt[3]{x\times0.000009}})^2=( 0.3)^2$ [On squaring both sides]
$\Rightarrow ( \sqrt[3]{x\times0.000009})=( 0.09)$
$\Rightarrow ( \sqrt[3]{x\times0.000009})^3=( 0.09)^3$ [Take cube of both sides]
$\Rightarrow ( x\times0.000009)=0.09\times0.09\times0.09$
$\Rightarrow x=\frac{0.09\times0.09\times0.09}{0.000009}$
$\Rightarrow x=81$
Therefore, $\sqrt{x}=\sqrt{81}$
$\Rightarrow \sqrt{x}=9$
Thus, $\sqrt{x}=9$.
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