# What is #root(3)x-1/(root(3)x)?#

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Please explain me how it says #root(3)xroot(3)x=x^(2/3)#

Please explain me how it says

##### 2 Answers

Take out the

Make their denominators same

#root(3)x*root(3)x=root(3)(x*x)=root(3)(x^2)=x^(2/3)#

#### Explanation:

Look at these alternative ways of writing roots

So for any number

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Just picking a number at random I chose 3

Another way (not normally done) of writing 3 is

When you have

In the same way

In the same way

Notice that

Notice that

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Given that a way of writing square root of 3 is

Compare what happens in each of the following two rows

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From above we know that

But we have

This is the same as

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Backtrack for a moment and again think about

Like in

and

Then

Turning this back the other way

Practise and a lot of it will fix this in your mind. It will seem confusing at first but as you practise more and more it will suddenly click!

Hope this helps!!