Question

If $\sqrt{784}=28$, find the value of:
(i) $\sqrt{7.84}+\sqrt{78400}$
(ii) $\sqrt{0.0784}+\sqrt{0.000784}$

Answer 1

(i) $\sqrt{7.84}+\sqrt{78400}$

$=\sqrt{\frac{784}{100}}+\sqrt{784\times 100}$

$=\frac{28}{10}+28\times 10$

$=2.8+280$

$=282.8$.
(ii) $\sqrt{0.0784}+\sqrt{0.000784}$

$=\sqrt{\frac{784}{{10}^4}}$$+\sqrt{\frac{784}{{10}^6}}$

$=\frac{28}{{10}^2}$$+\frac{28}{{10}^3}$

$=0.28+0.028$

$=0.308$