Question

Solve the following:
$\sqrt{{25}^{\frac{1}{{\log }_{8}5}}+{49}^{\frac{1}{{\log }_{8}7}}}$

Answer 1

$\sqrt{{25}^{\frac{1}{{\log }_{8}5}}+{49}^{\frac{1}{{\log }_{8}7}}}$ ....... $\left(i\right)$

$(5^2{)}^{{\log }_{5}8}$ $=8^2$

$(7^2{)}^{{\log }_{7}8}$ $=8^2$

Substitute the value in $\left(i\right)$, we get

$\sqrt{8^2+8^2}$ $=\sqrt{128}$ which can be also written as

$8\sqrt{2}$