Question

How do you rationalize the denominator and simplify `8/sqrt2`?

Answer 1

`4sqrt2`

Explanation:

`color(blue)"Rationalising"` the denominator means 'removing' the radical from the denominator and leaving a rational value in it's place.

To do this we make use of the following fact.

`color(red)(|bar(ul(color(white)(a/a)color(black)(sqrtaxxsqrta=a)color(white)(a/a)|)))`

`rArrsqrt2xxsqrt2=2" a rational number"`

Since this is a fraction we must also multiply the numerator by `sqrt2`

`rArr8/sqrt2=8/sqrt2 xx(sqrt2)/(sqrt2)`

`=(8sqrt2)/2=(cancel(8)^4 sqrt2)/cancel(2)^1=4sqrt2" in simplest form"`