Question

Use the properties of exponents to generate an equivalent expression for 3 over the square root of 8 as the numinator and 2 in a square root as the denominator

Answer 1

To simplify the expression \(\frac{3}{\sqrt{8}}\) and express it in a form with a square root in the denominator, we can use the properties of exponents and manipulate the expression.

First, let's rewrite \(\sqrt{8}\):

\[
\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}
\]

Now, we have:

\[
\frac{3}{\sqrt{8}} = \frac{3}{2\sqrt{2}}
\]

Next, we can rationalize the denominator by multiplying the numerator and denominator by \(\sqrt{2}\):

\[
\frac{3}{2\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{3\sqrt{2}}{2 \cdot 2} = \frac{3\sqrt{2}}{4}
\]

Thus, an equivalent expression for \(\frac{3}{\sqrt{8}}\) where \(2\) appears in the square root in the denominator is:

\[
\frac{3\sqrt{2}}{4}
\]