If $\sqrt{784} = 28$, find the value of $\sqrt{7.84} + \sqrt{78400}$

$\sqrt{7.84} + \sqrt{78400}\\[1em] = \sqrt{\dfrac{784}{100}} + \sqrt{784 \times 100}\\[1em] = {\dfrac{\sqrt{784}}{\sqrt{100}}} + ({\sqrt{784} \times \sqrt{100}})\\[1em] = {\dfrac{28}{10}} + ({28 \times 10})\\[1em] = 2.8 + 280\\[1em] = 282.8$

$\sqrt{7.84} + \sqrt{78400} = 282.8$.