Question
Simplify. Assume \( h \) is greater than or equal to zero. \[ \sqrt{8 h} \]
Ask by Christensen Bartlett. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
2\sqrt{2h}
\]
Solution
To simplify the expression \(\sqrt{8h}\) with the assumption that \(h \geq 0\), follow these steps:
1. **Factor the number inside the square root:**
\[
\sqrt{8h} = \sqrt{4 \times 2h}
\]
2. **Separate the square root of the product into the product of square roots:**
\[
\sqrt{4 \times 2h} = \sqrt{4} \times \sqrt{2h}
\]
3. **Simplify \(\sqrt{4}\) since it's a perfect square:**
\[
\sqrt{4} = 2
\]
4. **Combine the results:**
\[
2 \times \sqrt{2h} = 2\sqrt{2h}
\]
So, the simplified form of \(\sqrt{8h}\) is:
\[
2\sqrt{2h}
\]
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Simplify this solution Extra Insights
To simplify \( \sqrt{8h} \), we can first break down the expression inside the square root. The number 8 can be expressed as \( 4 \times 2 \), so we have: \[ \sqrt{8h} = \sqrt{4 \times 2 \times h} \] Since \( \sqrt{4} \) is 2, we can rewrite the expression as: \[ \sqrt{8h} = \sqrt{4} \cdot \sqrt{2} \cdot \sqrt{h} = 2 \sqrt{2h} \] Thus, the simplified form of \( \sqrt{8h} \) is: \[ 2\sqrt{2h} \]
