Question

How do you simplify `3/ sqrt 2`?

Answer 1

`3/(sqrt2)=color(blue)((3sqrt2)/2`

Explanation:

Simplify:

`3/(sqrt2)`

Rationalize the denominator by multiplying the numerator and denominator by `sqrt2`.

`(3sqrt2)/(sqrt2sqrt2)`

Apply rule: `sqrtasqrta=a`

`(3sqrt2)/2`

Answer 2

`(3sqrt2)/2`

Explanation:

It is considered good mathematical practice if you do not have any roots in the denominator. So lets 'get rid' of it!

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

`color(green)(3/sqrt2color(red)(xx1) color(white)("ddd")->color(white)("ddd")3/sqrt2color(red)(xxsqrt2/sqrt2)color(white)("d")=color(white)("d")(3sqrt2)/2)`