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Simplify \( \sqrt{32} \) \( \begin{array}{ll}\text { A) } 2 \sqrt{2} & \text { C) } 8 \sqrt{2} \\ \text { B) } 2 \sqrt{16} & \text { D) } 4 \sqrt{2}\end{array} \)

Ask by Gardner Mullins. in the United States
Feb 27,2025

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Tutor-Verified Answer

Answer

The simplified form of √32 is 4√2.

Solution

To simplify √32, look for the largest perfect square factor of 32. Notice that 32 = 16 × 2, where 16 is a perfect square. Thus:  √32 = √(16×2) = √16 × √2 = 4√2 The correct answer is D) 4√2.

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Bonus Knowledge

First, let's break down \( \sqrt{32} \). We can factor 32 as \( 16 \times 2 \), which allows us to rewrite the square root: \[ \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4 \sqrt{2}. \] So the answer is clearly \( D) 4 \sqrt{2} \)! Remember, simplifying square roots can often involve breaking numbers down into their prime factors. When you see a perfect square, like 16 in this case, it’s always worth pulling it out to make the expression easier.

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