Question

If the square root of the cube root of $x$ is $3$, find the value of $x$.

• A. $3$
• B. $9$
• C. $27$
• D. $729$

Answer 1

Answer: (D)

$729$

Given, cube root of $x$ is $\sqrt[3]{3x}=x^{\frac{1}{3}}$ and square root of it is $\sqrt{x^{\frac{1}{3}}}={\left(x^{\frac{1}{3}}\right)}^{\frac{1}{2}}=x^{(\frac{1}{3}\times \frac{1}{2})}=x^{\frac{1}{6}}=3$
Therefore $x=3^6=729$