What is 2 3/2 equal to?

Mathematics

1 answer:

kati45 [8]1 year ago

6 0

Answer:

(a) √8

Step-by-step explanation:

You want to know the radical equivalent to 2^(3/2).

<h3>Indices</h3>

The relationship of indices to radicals is ...

$\large{\sqrt[n]{a^m}}={a^{\frac{m}{n}}$

<h3>Application</h3>

The given expression can be rewritten as ...

$2^{\frac{3}{2}}=\sqrt[2]{2^3}=\boxed{\sqrt[2]{8}}$

<em>Additional comment</em>

When the index of the radical is 2, it is usually left off. The radical can be simplified by removing the perfect square factor.

$\sqrt[2]{8}=\sqrt{8}=2\sqrt{2}$

You might be interested in

The bottom portion of a loading bin is cone shaped. The base radius of this part of the bin is 3.5 feet and the slant height is

jek_recluse [69]

$\bf \textit{lateral surface of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} ~~ r=radius\\ sh=\stackrel{slant~height}{\sqrt{r^2+h^2}}\\[-0.5em] \hrulefill\\ r=3.5\\ sh=6.5 \end{cases}\\\\\\ LA=\pi (3.5)(6.5)\implies LA\approx71.47 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{sh}{6.5}=\sqrt{r^2+h^2}\implies 6.5=\sqrt{3.5^2+h^2}\implies 6.5^2=3.5^2+h^2 \\\\\\ 6.5^2-3.5^2=h^2\implies \sqrt{6.5^2-3.5^2}=h\implies \sqrt{30}=h \\\\[-0.35em] ~\dotfill$

$\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3.5\\ h=\sqrt{30} \end{cases}\implies V=\cfrac{\pi (3.5)^2\sqrt{30}}{3}\implies V\approx 70.26$