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

May 4, 2016

#### Explanation:

The set of rational numbers Q are expressed in the form $\frac{a}{b}$

where a,b inZ, b≠0

now 4 is in this form ie. $\frac{4}{1} \Rightarrow \text{ in rational form }$

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

For example , if $\sqrt{6} - 3 \text{ was on the denominator }$

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

$\Rightarrow \left(\sqrt{6} - 3\right) \left(\sqrt{6} + 3\right) = {\left(\sqrt{6}\right)}^{2} + 3 \sqrt{6} - 3 \sqrt{6} - 9$

$= 6 - 9 = - 3 \text{ a rational value }$