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Title
Percent with Roots
Your Result
Correct
Difficulty
Hard
Your Pace
2:04
Others' Pace
1:25
Video Explanation
Text Explanation
This is a very tricky question, combining a few tricky ideas. The first tricky issue is the idea of A% of B. Under ordinary circumstances, if we wanted, say, 17% of something, we would change that percent to a decimal by sliding the decimal place over --- 0.17 --- and then we would multiply by that decimal. Here, we can't do that, because the percent is not a whole number but rather a radical expression. Therefore, we have to change, not to a decimal, but to a fraction: A% is equivalent to (A/100), so we divide the percent number by 100 and multiply
Normally, I would recommend any possible canceling to simplify --- for example, the 5 and the 100 could be cancelled ---BUT I notice that all the answers are in decimal form, not fraction form, so it will be useful to keep all the powers of ten in the denominator. Even though we could, we will not cancel the 5 and the 100.
Instead, let's talk about those radicals. I'm going to rearrange the fraction multiplication a little:
Now, that fraction on the right can be simplified. This is the other tricky idea in the problem: we can combine or separate radicals by multiplication or division.
Therefore, we can simplify that fraction of radicals:
Answer = A
Related Lessons
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