Rank the following quantities in order, from smallest to biggest.
I. $\frac{2}{3}$
II. $\sqrt{\frac{5}{9}}$
III. $\sqrt[5]{\frac{5}{9}}$

Answer Choices

Correct answer marked below

I, II, III

Correct

I, III, II

II, I, III

III, I, II

III, II, I

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Preview

Official Explanation

Official

First of all, clearly

\sqrt{\frac{2}{3}} = \sqrt{\frac{4}{9}} < \sqrt{\frac{5}{9}}

. So, II is bigger than I.

Now, what about III? When we take higher order roots, the values move closer to one. If the number starts larger than one, then higher and higher roots make it smaller, closer to one. If the number starts between 0 and 1, then higher and higher roots make it larger, closer to one.…

Read the full explanation

Create free account Sign in

Comments

No comments yet

Be the first to share your thoughts and help others understand it better.

What this question tests

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.

Rank the following quantities in order, from smallest to biggest.I. 23\frac{2}{3}32​II. 59\sqrt{\frac{5}{9}}95​​III. 595\sqrt[5]{\frac{5}{9}}595​​