Question

Find the value of $\sqrt{7\left(\sqrt{7\sqrt{7}}\right)}$

• A.
• B.
• C. 7²
• D.

Answer 1

The correct option is B

Given Number $\sqrt{7\left(\sqrt{7\sqrt{7}}\right)}$

= $\sqrt{7.\sqrt{7\times 7^{\frac{1}{2}}}}$

= $\sqrt{7.\sqrt{7^{\frac{3}{2}}}}$

= $\sqrt{7.\sqrt{7^{\frac{3}{2}\times \frac{1}{2}}}}$

= $\sqrt{7^{1+\frac{3}{4}}}$

= $7^{\frac{7}{4}\times \frac{1}{2}}$

= $7^{\frac{7}{8}}$