If √4096 = 64, then the value of √40.96 + √0.004096 + √0.00004096 up to two place of decimals is = ?

17.09
27.10
37.11
47.12

Answer:- 1

Explanation:-

Solution:

\begin{aligned} According to question \\ \sqrt{40.96} + \sqrt{0.4096} + \sqrt{0.004096} + \sqrt{0.00004096} \\ \Rightarrow \sqrt{\frac{4096}{100}} + \sqrt{\frac{4096}{10000}} + \sqrt{\frac{4096}{1000000}} + \sqrt{\frac{4096}{100000000}} \\ \Rightarrow \frac{64}{10} + \frac{64}{100} + \frac{64}{1000} + \frac{64}{10000} \\ \Rightarrow 6.4 + 0.64 + 0.064 + 0.0064 \\ \Rightarrow 7.11 \end{aligned}

$\eqalign{ & {\text{According to question}} \cr & \sqrt {40.96} {\text{ + }}\sqrt {0.4096} {\text{ + }}\sqrt {0.004096} {\text{ + }}\sqrt {0.00004096} \cr & \Rightarrow \sqrt {\frac{{4096}}{{100}}} + \sqrt {\frac{{4096}}{{10000}}} + \sqrt {\frac{{4096}}{{1000000}}} + \sqrt {\frac{{4096}}{{100000000}}} \cr & \Rightarrow \frac{{64}}{{10}} + \frac{{64}}{{100}} + \frac{{64}}{{1000}} + \frac{{64}}{{10000}} \cr & \Rightarrow 6.4 + 0.64 + 0.064 + 0.0064 \cr & \Rightarrow 7.11 \cr}$