[3]4; 3; [6]25; [12]289 What are the greatest… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Roots

{ $\sqrt[3]{4}$ ; $\sqrt{3}$ ; $\sqrt[6]{25}$ ; $\sqrt[{12}]{289}$ } What are the greatest and the least number, respectively from the list above?

Answer Choices

Correct answer marked below

\sqrt[{12}]{289}

and

\sqrt[3]{4}

\sqrt{3}

and

\sqrt[3]{4}

Correct

\sqrt[6]{25}

and

\sqrt{3}

\sqrt[3]{4}

and

\sqrt[6]{25}

\sqrt[6]{25}

and

\sqrt[{12}]{289}

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Explanation

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Official Explanation

Official

Let's look at the powers of all the roots. Powers are

\frac{1}{3}

\frac{1}{2}

\frac{1}{6}

and

\frac{1}{12}

for {

\sqrt[3]{4}

;

\sqrt{3}

;

\sqrt[6]{25}

;

\sqrt[{12}]{289}

} respectively.

Since all are roots of a number, all values are positive.

Theory: When comparing positive numbers, it is same as comparing powers of those positive numbers.

We need to take LCM of all the roots i.e. we need to take LCM of 2, 3, 6 and 12. We are doing this as we can raise all the fractions to LCM to convert them to integer powers (so that it is easier to calculate and compare them!).…

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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.

{43\sqrt[3]{4}34​; 3\sqrt{3}3​; 256\sqrt[6]{25}625​; 28912\sqrt[{12}]{289}12289​} What are the greatest and the least number, respectively from the list above?