# rationalising denominators

• Jan 16th 2010, 02:26 AM
andyboy179
rationalising denominators
hi, i need to rationalise the denominator of this, $\displaystyle \frac{1}{2\sqrt{3}}$

how would i work this out?
• Jan 16th 2010, 02:54 AM
pickslides
Here's one I prepared earlier.

Consider

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

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

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

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

So lets make it the following

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

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

Now we have

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

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

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

Apply this method to your problem.
• Jan 16th 2010, 03:00 AM
andyboy179
Quote:

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

Consider

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

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

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

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

So lets make it the following

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

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

Now we have

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

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

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

Apply this method to your problem.

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

but i don't understand how to get the answer
• Jan 16th 2010, 03:09 AM
pickslides
Quote:

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

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 $\displaystyle \frac{a}{b}\times \frac{c}{d} = \frac{a\times c}{b\times d}$
• Jan 16th 2010, 03:13 AM
andyboy179
Quote:

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

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

would the answer to my question be, Attachment 14842 ?
• Jan 16th 2010, 03:23 AM
pickslides
Yes, yes it is

(Clapping)
• Jan 16th 2010, 03:26 AM
andyboy179
thank you so much, you'd make a great teacher!!!
• Jan 16th 2010, 03:30 AM
andyboy179
oh ye one others thing, is this right? Attachment 14844
• Jan 16th 2010, 03:34 AM
mr fantastic
Quote:

Originally Posted by andyboy179
oh ye one others thing, is this right? Attachment 14844

Yes.