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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Updated on: 10-Oct-2022

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