Why is $\sqrt{8}/2$ equal to $\sqrt{2}$?

Solution 1:

I am a bit surprised that nobody suggested $$\left({\frac{\sqrt 8}2}\right)^2 = \frac{{\left(\sqrt 8\right)}^2}{2^2} = \frac84 = 2. $$

Solution 2:

It isn't, as originally written. To see why the fixed version is correct, we have:

$$\frac{\sqrt{8}}2=\frac{\sqrt{4\cdot2}}2=\frac{\sqrt{4}\sqrt{2}}2=\frac{2\sqrt{2}}2=\sqrt{2}.$$

Solution 3:

It’s simple:

$$\frac{\sqrt{8}}{2} = \frac{\sqrt{2 \cdot 2 \cdot 2}}{\sqrt{2 \cdot 2}} = \sqrt{2}$$

:)

Solution 4:

$$\frac{\sqrt8}{2}=\frac{\sqrt8}{\sqrt{2^2}}=\sqrt{\frac{8}{2^2}}=\sqrt{\frac{8}{4}}=\sqrt2.$$

Solution 5:

By noting that $2^3 =8$, you have $$\frac{\sqrt{8}}{2} = \frac{\sqrt{2^3}}{2} = \frac{ 2^{3/2}}{2} = 2^{1/2}=\sqrt{2} \neq \sqrt{4}$$