Question

Fill in the blanks:

ii) $\sqrt[3]{38\times ....}=8$

Answer 1

Step: Fill in the blank

Given:$\sqrt[3]{38\times ....}=8$

Let, the required number be $x$.

$\therefore \sqrt[3]{38\times x}=8$

$\Rightarrow \sqrt[3]{38}\times \sqrt[3]{3x}=8$ $\because \sqrt[3]{3a\times b}=\sqrt[3]{3a}\times \sqrt[3]{3b}$

$\Rightarrow \sqrt[3]{32\times 2\times 2}\times \sqrt[3]{3x}=8$

$\Rightarrow 2\times \sqrt[3]{3x}=8$

$\Rightarrow \sqrt[3]{3x}=4$

$\therefore x=4^3=64$ (Taking cube on both the side)

Hence, the correct answer is $64$.