What is the value of ?
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Wait, the choices all have a percent sign. Does that mean the answer should be expressed as a percentage? Like, if I get 1/√2, should I write it as (1/√2)%? That seems odd because the original is a ratio of percentages, so it should be unitless.
I think the percent sign in the choices is just a unit label, but it's confusing. The question asks for the value, so probably the number without percent. But then why all choices have %? Maybe it's a trick.
Yeah, I got confused too. I think the answer choices are meant to be read as the number followed by percent sign, but the actual value is just the number. So (B) would be 1/√2, but they wrote it as (1/√2)%. That's weird.
I simplified 20%/40% to 1/2, then sqrt(1/2) = 1/√2. But none of the answers match exactly unless I multiply by something. What am I missing?
Maybe you need to convert the percentages to decimals first? 20% = 0.2, 40% = 0.4, so 0.2/0.4 = 0.5, sqrt(0.5) = 1/√2 ≈ 0.707. Still doesn't match any answer choices directly.
Check the answer choices again: (B) is (1/√2)%. If you interpret that as 1/√2 percent, that's 0.707%, which is 0.00707. But our answer is 0.707. So maybe they want the answer as a percentage? That would be 70.7%, which is not listed. I'm stuck.
This is a tricky one because of the percent signs. I think the key is to realize that 20% = 20/100 = 0.2, so 20%/40% = 0.2/0.4 = 0.5. Then sqrt(0.5) = 1/√2. But the answer choices are in percent, so we need to express 1/√2 as a percentage? That would be (1/√2)*100% = (100/√2)% = (50√2)%. That's choice (D). But wait, is that correct?
Yes, that's what I got too. But why would they ask for the value in percent when the original expression is a ratio? It seems like an extra step.
I think the question is designed to test if you notice the percent signs in the answer choices. The original expression is unitless, but the answer choices have percent, so you have to convert. It's a bit of a trap.
I got (D) but I'm not 100% sure. Can someone confirm if we need to multiply by 100% at the end?
I think so. Because sqrt(20%/40%) = sqrt(0.5) = 1/√2. To express as a percentage, multiply by 100%: (100/√2)% = (50√2)%. So (D).
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.