Simple comparison (part 2)

Algebra Level 2

Fact: $\begin{aligned} \sqrt{32} &= 5.656\ldots \\ \sqrt[3]{181} &= 5.656\ldots. \end{aligned}$

But which is larger, $\sqrt{32}$ or $\sqrt[3]{181}?$

\sqrt{32}

\sqrt[3]{181}

They are equal

2 solutions

Denton Young
Dec 12, 2017

C = $\sqrt[6]{32^3} = \sqrt[6]{32768}$

D = $\sqrt[6]{181^2} = \sqrt[6]{32761}$

C > D

Bullshit. The instructions say to use your brain and not a calculator. I know math and how it works. Give me a calculator and I can do it. I'm not a math whiz and can't calculate 3rd roots in my head.

Lisa MacDonald - 3 years, 5 months ago

You don't have to. You just have to be able to cube 32 (or double 2 14 times, which is what I did), and then square 181. The latter I used scrap paper for, so I'm wondering if there's an easier way. 181 is prime for whatever that's worth.

Rishabh Iyer - 3 years, 5 months ago

Calm down, square a small number you don't need calculator. You an idiot.

Peter Backstrand - 3 years, 5 months ago

Aishwary Omkar
Jan 9, 2018

One way is to cube the numbers. 32 $\sqrt{32}$ = 181.024 > 181 And y=x^3 is a monotonically increasing function which implies that $\sqrt{32}$ ) is bigger

Simple comparison (part 2)

2 solutions

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