What is the value of ( 7+ 29- 7-[ 29])^2 | GMAT Sprint

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PS · Problem Solving

605-655

Arithmetic

What is the value of $(\sqrt{7+\sqrt29}-\sqrt{7-[\sqrt{29}]})^2$

Correct answer marked below

-26

2\sqrt{29}

14-4\sqrt{5}

Correct

14

14-5\sqrt{5}

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Explanation

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Official Explanation

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We are asked to evaluate:

\left( \sqrt{7 + \sqrt{29}} - \sqrt{7 - \sqrt{29}} \right)^2

Step 1: Use identity

(a - b)^2 = a^2 - 2ab + b^2

Let:

a = \sqrt{7 + \sqrt{29}}, \quad b = \sqrt{7 - \sqrt{29}}

Then:

(a - b)^2 = a^2 + b^2 - 2ab

**Step 2: Compute

a^2

and

b^2

a^2 = 7 + \sqrt{29}, \quad b^2 = 7 - \sqrt{29}

…

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What this question tests

Your fluency with the order of operations, fractions, decimals, and basic number sense — the foundation every quant question leans on.

Applying the order of operations out of sequence or rounding intermediate values before the final step.