To express [tex]\(\sqrt{8}\)[/tex] in the form [tex]\(2^n\)[/tex], we can follow these steps:
1. Express 8 as a power of 2:
[tex]\[
8 = 2^3
\][/tex]
2. Take the square root of both sides:
[tex]\[
\sqrt{8} = \sqrt{2^3}
\][/tex]
3. Use the property of exponents for square roots [tex]\(\sqrt{a^b} = a^{b/2}\)[/tex]:
[tex]\[
\sqrt{2^3} = 2^{3/2}
\][/tex]
Therefore, we have:
[tex]\[
\sqrt{8} = 2^{3/2}
\][/tex]
So, [tex]\(n\)[/tex] equals [tex]\(\frac{3}{2}\)[/tex] or 1.5.
In conclusion, [tex]\(\sqrt{8}\)[/tex] can be expressed in the form [tex]\(2^n\)[/tex] where [tex]\(n = \frac{3}{2}\)[/tex].
