Question

please answer with explaination​

Answer 1

$\texttt{\textsf{\large{\underline{Solution}:}}}$

We have to evaluate –

$\tt = \sqrt[3]{\dfrac{ {3}^{3} \times {7}^{3} \times {5}^{9} }{ {10}^{6} }}$

Cube root of a number is equal to the number raised to the power 1/3. So,

$\tt = \dfrac{ \sqrt[3]{ {3}^{3} } \times \sqrt[3]{{7}^{3}} \times \sqrt[3]{{5}^{9}} }{ \sqrt[3]{{10}^{6}}}$

$\tt = \dfrac{ {3}^{3 \times ^{1}/_{3}} \times {7}^{3 \times ^{1}/_{3}} \times {5}^{9 \times ^{1}/_{3}} }{ {10}^{6 \times ^{1}/_{3}} }$

$\tt = \dfrac{3\times 7\times {5}^{3}}{ {10}^{2} }$

$\tt = \dfrac{21\times 125}{100}$

$\tt = \dfrac{2625}{100}$

$\tt =26.25$

Which is our required answer.

$\texttt{\textsf{\large{\underline{Answer}:}}}$

• Result = 26.25