Simplify \(\frac{\sqrt{45 + \sqrt{1}} + \sqrt{45 + \sqrt{2}} + \sqrt{45 + \sqrt{3}} + \dots + \sqrt{45 + \sqrt{2024}}}{\sqrt{45 - \sqrt{1}} + \sqrt{45 - \sqrt{2}} + \sqrt{45 - \sqrt{3}} + \dots + \sqrt{45 - \sqrt{2024}}}\)

Guest Jan 27, 2019

#1**0 **

Assuming that the numberator is the same as the denominator, the answer is \(\boxed{1}\).

Treat \(\sqrt{45 + \sqrt{1}} + \sqrt{45 + \sqrt{2}} ... + \sqrt{45 + \sqrt{2024}}\) as X. We will have \(\dfrac{X}{X}\), which simplifies into 1.

Hope this helps,

- PM

PartialMathematician Jan 27, 2019