Question
\( \sqrt{150}=\square \) (Simplify your answer. Type an exact answer, using radicals as needed.)
Ask by Vaughan Salazar. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 5\sqrt{6} \)
Solution
1. Factor the radicand:
\[
150 = 25 \times 6
\]
2. Apply the property of square roots:
\[
\sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6}
\]
3. Simplify:
\[
\sqrt{25} = 5
\]
Therefore,
\[
\sqrt{150} = 5\sqrt{6}
\]
Final answer:
\[
5\sqrt{6}
\]
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Simplify this solution Extra Insights
To simplify \( \sqrt{150} \), we can start by breaking down 150 into its prime factors. We have \( 150 = 2 \times 3 \times 5^2 \). Now, we can re-write \( \sqrt{150} \) using these factors: \[ \sqrt{150} = \sqrt{2 \times 3 \times 5^2} \] We can simplify this further because \( \sqrt{5^2} = 5 \): \[ \sqrt{150} = 5 \times \sqrt{2 \times 3} \] \[ = 5 \sqrt{6} \] So, the simplified form of \( \sqrt{150} \) is \( 5\sqrt{6} \).
