# Square roots and fractions

How do you get 3/sqrt2 from 3sqrt2/2?

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Math Is Hard
Staff Emeritus
Gold Member
hint: sqrt2/sqrt2 = 1

sorry dont follow

Integral
Staff Emeritus
Gold Member
Try going the other way.
$$\frac 3 {\sqrt 2}$$

to get

$$\frac {3 \sqrt 2} 2$$

If you're going from 3sqrt2/2 to 3/sqrt2 you're basically de-rationalizing the denominator.

HallsofIvy
Homework Helper
By definition $(\sqrt{2})^2= \sqrt{2}\sqrt{2}= 2$. That means that
$$\frac{\sqrt{2}}{2}= \frac{\sqrt{2}}{\sqrt{2}\sqrt{2}}$$

Air
Ry122 said:
How do you get 3/sqrt2 from 3sqrt2/2?
$\frac{3}{\sqrt 2} . \frac{\sqrt 2}{\sqrt 2} = \frac{3 \sqrt 2}{2}$.

This is rationalising the denominator as you cannot have a surd on the denominator. The question that you are asking is how you get the reverse, de-rationalising the denominator. Try opposite steps to the one I shown.