Pregunta
Simplify the product. \[ \sqrt{5} \cdot \sqrt{20} \]
Ask by Howell Chang. in the United States
Jan 22,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The product simplifies to 10.
Solución
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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Simplifique esta solución 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: \[ \boxed{10} \]
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