Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\sqrt{300} = 10\sqrt{3}
\]
Solution
To simplify the expression \(\sqrt{300}\), follow these steps:
1. **Factor the Number Inside the Square Root:**
Break down 300 into its prime factors or look for perfect squares that divide 300.
\[
300 = 100 \times 3
\]
Here, 100 is a perfect square because \(100 = 10^2\).
2. **Apply the Square Root to Each Factor:**
\[
\sqrt{300} = \sqrt{100 \times 3} = \sqrt{100} \times \sqrt{3}
\]
3. **Simplify the Square Roots:**
\[
\sqrt{100} = 10
\]
So,
\[
\sqrt{300} = 10 \times \sqrt{3} = 10\sqrt{3}
\]
**Final Answer:**
\[
\sqrt{300} = 10\sqrt{3}
\]
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Simplify this solution Beyond the Answer
To simplify \( \sqrt{300} \), we first factor 300 into its prime factors. We can write: \[ 300 = 3 \times 100 = 3 \times 10^2 = 3 \times (2 \times 5)^2 = 3 \times 2^2 \times 5^2. \] Now, we can apply the square root: \[ \sqrt{300} = \sqrt{3 \times 100} = \sqrt{3} \times \sqrt{100} = \sqrt{3} \times 10 = 10\sqrt{3}. \] So, the simplified form of \( \sqrt{300} \) is: \[ 10\sqrt{3}. \]
