How can you de-rationalise the denominator of 3sqrt2/2?

[Ry122]

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

 

[scarecrow]

Ask yourself what's (sqrt x)^2?

 

[Math Is Hard]

hint: sqrt2/sqrt2 = 1

 

[Ry122]

sorry don't follow

 

[Integral]

Try going the other way.
Start with
$$\frac 3 {\sqrt 2}$$

to get

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

 

[Feldoh]

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

 

[HallsofIvy]

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]

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.