Question

Use the properties of exponents to generate an equivalent expression for 3√8/√2

Find the cube root of 8. Then, rewrite rational exponents as radicals and simplify.

Answer 1

To simplify the expression \( \frac{\sqrt[3]{8}}{\sqrt{2}} \), let's go through the steps as mentioned:

1. **Find the cube root of 8:**
The cube root of \( 8 \) is \( 2 \), since \( 2^3 = 8 \). Therefore, we have:
\[
\sqrt[3]{8} = 2
\]

2. **Rewrite the expression:**
Now we can substitute this value back into the expression:
\[
\frac{\sqrt[3]{8}}{\sqrt{2}} = \frac{2}{\sqrt{2}}
\]

3. **Simplify \(\frac{2}{\sqrt{2}}\):**
To simplify \( \frac{2}{\sqrt{2}} \), we can multiply the numerator and the denominator by \( \sqrt{2} \):
\[
\frac{2}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{2}
\]
This simplifies to:
\[
\sqrt{2}
\]

So, the equivalent expression for \( \frac{\sqrt[3]{8}}{\sqrt{2}} \) is \( \sqrt{2} \).