$\sqrt{9 + 4√5} + \sqrt{30 − 10√5}$ =

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Correct

3 + 2\sqrt{5}

19.5 − 3\sqrt{5}

39 − 6\sqrt{5}

140 − 60\sqrt{5}

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Explanation

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Official Explanation

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Approximate value

\sqrt{5}=2.2

\sqrt{9 + 4√5} + \sqrt{30 − 10√5}

\sqrt{9 + 4*2.2} + \sqrt{30 − 10*2.2}

\sqrt{17.8} + \sqrt{7.8}

This is surely greater than 4+2 or 6 and less than 5+3 or 8. So A or B.

Solve the expression:

It is a square root so we have to check whether we can make the terms that are under square root as squares.…

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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.

9+4√5+30−10√5\sqrt{9 + 4√5} + \sqrt{30 − 10√5} 9+4√5​+30−10√5​ =