# Thread: rationalising denominators

1. ## rationalising denominators

hi, i need to rationalise the denominator of this, $\frac{1}{2\sqrt{3}}$

how would i work this out?

2. Here's one I prepared earlier.

Consider

$\frac{1}{4\sqrt{5}}$

Let's times it by 1 because that won't change anything

$\frac{1}{4\sqrt{5}}\times 1$

But 1 comes in many forms I.e $\frac{a}{a}=1, a\neq 0$

So lets make it the following

$\frac{1}{4\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}$

I did this because $\sqrt{a}\times \sqrt{a}= a$

Now we have

$\frac{1\times \sqrt{5}}{4\sqrt{5}\times \sqrt{5}}$

$\frac{\sqrt{5}}{4\times 5}$

We have no radical in the denominator so we are finished.

Apply this method to your problem.

3. Originally Posted by pickslides
Here's one I prepared earlier.

Consider

$\frac{1}{4\sqrt{5}}$

Let's times it by 1 because that won't change anything

$\frac{1}{4\sqrt{5}}\times 1$

But 1 comes in many forms I.e $\frac{a}{a}=1, a\neq 0$

So lets make it the following

$\frac{1}{4\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}$

I did this because $\sqrt{a}\times \sqrt{a}= a$

Now we have

$\frac{1\times \sqrt{5}}{4\sqrt{5}\times \sqrt{5}}$

$\frac{\sqrt{5}}{4\times 5}$

We have no radical in the denominator so we are finished.

Apply this method to your problem.

$\frac{1}{2\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}$

but i don't understand how to get the answer

4. Originally Posted by andyboy179
$\frac{1}{2\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}$

but i don't understand how to get the answer
You have started the problem perfectly, now just follow what I have done in post #2.

Recall when multiplying fractions $\frac{a}{b}\times \frac{c}{d} = \frac{a\times c}{b\times d}$

5. Originally Posted by pickslides
You have started the problem perfectly, now just follow what I have done in post #2.

Recall when multiplying fractions $\frac{a}{b}\times \frac{c}{d} = \frac{a\times c}{b\times d}$
would the answer to my question be, ?

6. Yes, yes it is

7. thank you so much, you'd make a great teacher!!!

8. oh ye one others thing, is this right?

9. Originally Posted by andyboy179
oh ye one others thing, is this right?
Yes.