Of the following, which is the closest approximation to ?
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18^2=324, so it's a little less than 18. Closest is 20. Easy.
Yeah I did the same, but 17^2 is 289 and 20^2 is 400, so the answer is clearly 20.
Nice, I was stuck trying to actually estimate the decimal. This is way faster.
How do you even know to compare with 18^2? I was over here trying to find a perfect square near 320 and got lost in the decimals.
Just look for perfect squares around 320: 18^2=324, 17^2=289. Since 320 is between them, root is between 17 and 18.
Same, I wasted time trying to do long division. The key is the answer choices are far apart, so you just need a rough range.
The answer choices being so spread out makes this much easier. If they were like 17.5, 17.8 it would be brutal. Here you can just bound it between 17 and 18.
I got 20 but I'm not sure why 30 isn't just as close? Can someone explain the bounding?
30^2=900 which is way bigger than 320, so it can't be close. You need a number whose square is near 320.
You're right that 20^2=400 is farther from 320 than 18^2=324, but among the choices 20 is the closest. 30 is way off because 30^2=900.
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.