If x=20 and y=16, then x+ y x+y =

Free Practice Question

PS · Problem Solving

605-655

Roots

If $\sqrt{x}=20$ and $\sqrt{y}=16$ , then $\frac{\sqrt{x}+\sqrt{y}}{\sqrt{x+y}} =$

Answer Choices

Correct answer marked below

9\sqrt{41}

2

\frac{9\sqrt{41}}{41}

Correct

1

\frac{9}{41}

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Comments

MukhsanaJul 8

Thanks, I was overthinking this one. For some reason I kept trying to work with sqrt(x+y) as sqrt(x) + sqrt(y) and got nowhere.

ValenitJul 9

Same trap here. Took me a second to realize we already know the numerators.

SamiyahJul 21

Classic. I did that on my first attempt too and panicked when nothing matched.

RahulAug 11

Quick question — how do you get x + y once you find x and y? I got x = 400 and y = 256, but then I wasn't sure whether to leave it as 656 or simplify.

ThaoAug 15

You can take out a perfect square factor from 656 before combining with the top.

HungJul 11

Why is choice A tempting? It's like they knew people would forget to rationalize the denominator.

IgnacioJul 25

I picked A at first ngl. Sneaky.

DivyJun 7

This felt more like a 600-level problem once you see the numbers. Not bad at all.

SubhadityaJun 13

Agreed, the algebra is straightforward if you don't invent extra steps.

What this question tests

What it tests

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

Common trap

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

If x=20\sqrt{x}=20x​=20 and y=16\sqrt{y}=16y​=16, then x+yx+y=\frac{\sqrt{x}+\sqrt{y}}{\sqrt{x+y}} =x+y​x​+y​​=