Question

If $\sqrt{4096}=64$, what is the value of $\sqrt{40.96}+\sqrt{0.4096}+\sqrt{0.004096}+\sqrt{0.00004096}$.

Enter the nearest integer as answer.

Answer 1

$\sqrt{40.96}+\sqrt{0.4096}+\sqrt{0.004096}+\sqrt{0.00004096}=\sqrt{\frac{4096}{100}}+\sqrt{\frac{4096}{10000}}+\sqrt{\frac{4096}{1000000}}+\sqrt{\frac{4096}{100000000}}=\frac{\sqrt{4096}}{\sqrt{100}}+\frac{\sqrt{4096}}{\sqrt{10000}}+\frac{\sqrt{4096}}{\sqrt{1000000}}+\frac{\sqrt{4096}}{\sqrt{100000000}}=\frac{64}{10}+\frac{64}{100}+\frac{64}{1000}+\frac{64}{10000}=6.4+0.64+0.064+0.0064=7.1104$

Nearest inter to $7.1104$ will be $7$.