Question

How do you rationalize the denominator and simplify `(sqrt 6 - 3 ) / 4`?

Answer 1

denominator is already rationalised

Explanation:

The set of rational numbers Q are expressed in the form `a/b`

where a,b `inZ, b≠0`

now 4 is in this form ie. `4/1rArr " in rational form "`

Normally require to rationalise the denominator when the radical is on the denominator, which is not the case here.

For example , if `sqrt6 -3 " was on the denominator "`

Then to rationalise , we multiply by it's Conjugate

`• " conjugate of "sqrta ± b " is " sqrta ∓ b`

and multiplying by the conjugate produces a rational number

`rArr(sqrt6-3)(sqrt6+3)=(sqrt6)^2+3sqrt6-3sqrt6-9`

`=6-9=-3" a rational value "`