$\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?$

Answer Choices

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1.7

Correct

2.4

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Explanation

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Official Explanation

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Official Solution:

\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?

First, let's simplify the expression:

\sqrt{7 + \sqrt{48}} - \sqrt{3} = \sqrt{7 + \sqrt{16*3}} - \sqrt{3} = \sqrt{7 + 4\sqrt{3}} - \sqrt{3}

Observe that the answer choices are all rational numbers, so irrational parts in the expression must somehow cancel each other out. This observation should be a hint that we might be able to rewrite

7 + 4\sqrt{3}

in a way that makes it the square of something, which would allow us to extract the square root and simplify the expression.…

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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.

7+48−3=?\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?7+48​​−3​=?