The value of √{3√{0.046656}} is

Question

The value of \(\sqrt{\sqrt[3]{0.046656}}\) is

(a) 6

(b) 0.6

(c) 0.06

(d) 0.006

Answer 1

Correct option : (b) 0.6

\(\therefore 46656 =2^6 \times 3^6 =6^6\)

\(\therefore 0.046656 =\frac{46656}{10^6} =\frac{6^6}{10^6} =(\frac{6}{10})^6 =(0.6)^6\)

\(\therefore \sqrt{\sqrt[3]{0.046656}} =((0.046656)^\frac13)^\frac12\)

\(=((0.6)^6)^{\frac13\times\frac12}\)

\(=((0.6)^6)^\frac16 =(0.6)^{6\times\frac16} =0.6\)