Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\sqrt{20} = 2\sqrt{5} \approx 4.472
\]
Solution
To simplify \( \sqrt{20} \), you can follow these steps:
1. **Factor the Number Inside the Square Root:**
Break down 20 into its prime factors:
\[
20 = 4 \times 5
\]
Notice that 4 is a perfect square since \( 4 = 2^2 \).
2. **Apply the Square Root to Each Factor:**
\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5}
\]
3. **Simplify the Square Root of the Perfect Square:**
\[
\sqrt{4} = 2
\]
So,
\[
\sqrt{20} = 2 \times \sqrt{5} = 2\sqrt{5}
\]
**Final Answer:**
\[
\sqrt{20} = 2\sqrt{5}
\]
If you need a decimal approximation:
\[
\sqrt{5} \approx 2.236
\]
\[
2 \times 2.236 = 4.472
\]
So,
\[
\sqrt{20} \approx 4.472
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
Did you know that \( \sqrt{20} \) can be simplified? It breaks down to \( \sqrt{4 \times 5} \), and since the square root of 4 is 2, you can express it as \( 2\sqrt{5} \). This simplification makes it easier to use in calculations! In the real world, square roots are everywhere! From calculating distances in geometry to understanding concepts in physics, they help simplify complex problems. For example, in architecture, knowing the diagonal length of a space can be calculated using square roots to ensure structural integrity. Just think of square roots as handy tools for answering those “how far?” questions!
