Question

What is the simplest form 0f 2√2/√3-√2

Answer 1

`4+2√(6)`

Explanation:

Given expression is
`(2√(2))/(√(3)-√(2))`.

Now we need to simplify this. So multiply and divide by conjugate of denominator.

`(2√(2))/(√(3)-√(2))`

`=(2√(2))/(\left(√(3)-√(2)\right))`

`=(2√(2))/(\left(√(3)-√(2)\right))\cdot(\left(√(3)+√(2)\right))/(\left(√(3)+√(2)\right))`

`=(2√(6)+2√(4))/(\left(√(3)\right)^2-\left(√(2)\right)^2)`

`=(2√(6)+2\cdot2)/(3-2)`

`=(2√(6)+4)/(1)`

`=2√(6)+4`

`=4+2√(6)`

Hence final answer is
`4+2√(6)`.

Answer 2

`(2√(2))/(√(3)-√(2))=2√(6)+4`

Explanation:

We have the expression:

`(2√(2))/(√(3)-√(2))`

To simplify the expression multiply by the conjugate of the denominator.

The denominator is

`√(3)-√(2)`

Then its conjugate is:

`√(3)+√(2)`

Then:

`(2√(2))/(√(3)-√(2))*(√(3)+√(2))/(√(3)+√(2))\\\\=(2√(2)√(3)+2√(2)√(2))/((√(3))^2-(√(2))^2)\\\\(2√(6)+4)/(3-2)}\\\\= (2√(6)+4)/(1)}=2√(6)+4`