Question
Simplify the following exprossion If the expression cannot be simplifect, se state) \[ \sqrt{63} \] Select the correct choice below and, if mecessary, ill in the answer box to complete your choin A. \( \sqrt{63}= \) \( \square \) (Type an oxact answer, using radicals as noeded) B. The expression cannot be simplified
Ask by Flynn Floyd. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \sqrt{63} = 3\sqrt{7} \)
Solution
**A.** \( \sqrt{63} = 3\sqrt{7} \)
**Explanation:**
To simplify \( \sqrt{63} \), factor 63 into its prime factors:
\[
63 = 9 \times 7
\]
Since 9 is a perfect square (\( 9 = 3^2 \)), you can simplify the square root as follows:
\[
\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3\sqrt{7}
\]
Therefore, the simplified form of \( \sqrt{63} \) is \( 3\sqrt{7} \).
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Simplify this solution The Deep Dive
To simplify \(\sqrt{63}\), we can factor the number under the square root. Since \(63 = 9 \times 7\) and \(9\) is a perfect square, we can write it as \(\sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3\sqrt{7}\). So, the expression simplifies to: A. \( \sqrt{63} = 3\sqrt{7} \)
