Which of the following values is greater than ? i. ii. iii.
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Is there a quick way to compare these without a calculator? I started raising everything to the 30th power to compare, but that felt like overkill. Any tips?
Raising to the 30th power is actually a solid method. Since 30 is the LCM of 2, 3, 4, and 5, it makes the radicals disappear. Then you just compare the resulting integers.
Yeah, that's the standard approach. But you can also just approximate the values: sqrt2 ~1.414, cube root of 3 ~1.442, etc. That might be faster if you know your roots.
I got (D) i and iii, but I'm not 100% sure. Can someone confirm?
I also got i and iii. ii is exactly sqrt2, so it's not greater. i and iii are both slightly above sqrt2.
This was trickier than I expected. The exponents are all different, so you can't just compare the numbers under the roots directly. Had to think about it for a minute.
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.