Question

If $\sqrt{2916}=54$, what is the value of $\sqrt{29.16}+\sqrt{0.2916}+\sqrt{0.002916}+\sqrt{0.00002916}$

• A. $5.9949$
• B. $5.9894$
• C. $5.9984$
• D. $5.9994$

Answer 1

The correct option is D $5.9994$

$\sqrt{29.16}+\sqrt{0.2916}+\sqrt{0.002916}+\sqrt{0.00002916}$

$\Rightarrow$ $\sqrt{\frac{2916}{{10}^2}}+\sqrt{\frac{2916}{{10}^4}}+\sqrt{\frac{2916}{{10}^6}}+\sqrt{\frac{2916}{{10}^8}}$

$\Rightarrow$ $\frac{54}{10}+\frac{54}{100}+\frac{54}{1000}+\frac{54}{10000}$

$\Rightarrow$ $5.4+0.54+0.054+0.0054$

$\Rightarrow$ $5.9994$

$\therefore$ $\sqrt{29.16}+\sqrt{0.2916}+\sqrt{0.002916}+\sqrt{0.00002916}=5.9994$