Question

Find the value of $(\sqrt{64}+\sqrt{0.64}+\sqrt{0.0064})\times \sqrt{100}$.

Answer 1

The given expression can be written as
$\sqrt{64}+\sqrt{\frac{64}{100}}+\sqrt{\frac{64}{1000}}\times \sqrt{100}$

$=(\sqrt{8\times 8}+\sqrt{\frac{8\times 8}{10\times 10}}+\sqrt{\frac{8\times 8}{10\times 10\times 10\times 10})}\sqrt{10\times 10}$
$=(8+\frac{8}{10}+\frac{8}{10\times 10})\times 10$
$=(8+0.8+0.08)\times 10$
$=8.88\times 10$
$=88.8$