Question
Simplify the product. \[ \sqrt{5} \cdot \sqrt{20} \]
Ask by Howell Chang. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The product simplifies to 10.
Solution
To simplify the product \(\sqrt{5} \cdot \sqrt{20}\), you can use the property of square roots that states:
\[
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \times b}
\]
Let's apply this property step by step:
\[
\sqrt{5} \cdot \sqrt{20} = \sqrt{5 \times 20} = \sqrt{100}
\]
Now, simplify the square root of 100:
\[
\sqrt{100} = 10
\]
So, the simplified form of \(\sqrt{5} \cdot \sqrt{20}\) is:
\[
10
\]
**Answer:** \(10\)
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Simplify this solution Bonus Knowledge
To simplify the product \(\sqrt{5} \cdot \sqrt{20}\), we can use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\). Applying this property, we get: \[ \sqrt{5} \cdot \sqrt{20} = \sqrt{5 \cdot 20} \] Now, calculate \(5 \cdot 20\): \[ 5 \cdot 20 = 100 \] So, we have: \[ \sqrt{5} \cdot \sqrt{20} = \sqrt{100} \] Since the square root of 100 is 10, we simplify it to: \[ \sqrt{100} = 10 \] Therefore, the final result is: \[ \boxed{10} \]
