Question

Why is the square root of 8 the same as 4/square root of 2

Answer 1

sqrt 8 =2 sqrt2

Answer 2

It is the same... but which way would be the 'more correct' way to write it?

Answer 3

sqrt(8) = sqrt(2^3) = 2sqrt(2)

4/sqrt(2) =
\[ \frac{4}{\sqrt2} \]
\[ \frac{4}{\sqrt2} \times \frac{\sqrt2}{\sqrt2} \]
\[ \frac{4}{2} \times \sqrt{2} \]

check out http://www.oojih.com/show/algebra/exponentrationalradical/ for more about exponents formula

Answer 4

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

Answer 5

<img src=" http://latex.codecogs.com/gif.latex? \sqrt{8} = \frac{4}{\sqrt{2}}" title="\sqrt{8} = \frac{4}{\sqrt{2}}" />

raising to the power of 2 both sides

<img src=" http://latex.codecogs.com/gif.latex? \sqrt{8}^{2} = \left (\frac{4}{\sqrt{2}} \right )^{2}" title="\sqrt{8}^{2} = \left (\frac{4}{\sqrt{2}} \right )^{2}" />

thus

<img src=" http://latex.codecogs.com/gif.latex?8 = \left (\frac{16}{2} \right )" title="8 = \left (\frac{16}{2} \right )" />