$\sqrt[4]{\frac{99^2+101^2}{2}-1}=$

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Comments

GarvitaAug 7

Is there a trick to the inside part? I started expanding 99^2 and 101^2 and it got messy fast. There has to be a cleaner way, right?

JavierAug 18

Think about the two numbers being symmetric around 100. That usually simplifies things.

MarilenaAug 16

Yeah, don't expand. Let 100 be your anchor.

SaloniJun 16

Got it once I realized 99 = 100 - 1 and 101 = 100 + 1. The middle terms cancel nicely. Took me a minute to see it though.

DhairyaJun 22

Same here, the symmetry was the key for me too.

KasturikaAug 13

So after simplifying the inside I got 10000, then the fourth root just gives me the number. Pretty clean problem once you spot it.

SohamMay 12

Solid 600 level question. Not hard once you see the pattern, but easy to waste time brute forcing the squares.

What this question tests

Your handling of square and higher roots, including simplifying radicals.

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.

992+10122−14=\sqrt[4]{\frac{99^2+101^2}{2}-1}=42992+1012​−1​=