If x>0, then 1 x+ 2x=?

[m]\frac{1+\sqrt{2}}{\sqrt{x}}[/m]

Free Practice Question

PS · Problem Solving

555-605

Roots

If $x>0$ , then $\frac{1}{\sqrt{x}}+\sqrt{\frac{2}{x}}=$ ?

Answer Choices

Correct answer marked below

\frac{1}{3\sqrt{x}}

\frac{1}{2\sqrt{2x}}

\frac{1}{x\sqrt{2}}

\frac{\sqrt{2}-1}{\sqrt{x}}

\frac{1+\sqrt{2}}{\sqrt{x}}

Correct

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Explanation

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Comments

ElaMay 10

Thanks, this one was pretty quick once I noticed you can pull the 1/sqrt(x) out front. Nice confidence booster.

HimanshMay 18

Right, same here. The sqrt(2/x) part looked scary for a second but it splits nicely.

SheetalAug 17

Wait, how do you go from sqrt(2/x) to sqrt(2)/sqrt(x)? Is that just because the root of a fraction is the fraction of the roots?

AdyaAug 25

Yeah, sqrt(a/b) = sqrt(a)/sqrt(b) as long as b > 0, which the prompt gives us.

ShubhankarAug 21

Got it, that's the step I was missing, thanks!

SharleneJul 21

Solid 600-ish question. Nothing too crazy but the answer choices have enough lookalikes to punish a careless move.

AliJul 25

Exactly, I nearly picked the one with the minus sign before rechecking the addition.

NandhuMay 11

Is x > 0 given just so we don't have to worry about the denominator or negative roots? Seemed like extra info at first.

EakpreetMay 19

Pretty much, it keeps everything defined so you can factor without case work.

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>0x>0x>0, then 1x+2x=\frac{1}{\sqrt{x}}+\sqrt{\frac{2}{x}}=x​1​+x2​​=?