Question

Please help i dont understand what its asking

Answer 1

Multiply both the numerator and denominator by
`2+\sqrt3`, which is called the "conjugate" of
`2-\sqrt3`:

`(5+\sqrt3)/(2-\sqrt3)\cdot(2+\sqrt3)/(2+\sqrt3)`

Why do we pick this number? Recall the difference of squares factorization:

`a^2-b^2=(a-b)(a+b)`

Now replace
`a=2` and
`b=\sqrt3`. Then

`(2-\sqrt3)(2+\sqrt3)=2^2-(\sqrt3)^2=4-3=1`

So in your fraction, you end up with

`(5+\sqrt3)/(2-\sqrt3)=\frac{(5+\sqrt3)(2+\sqrt3)}1=(5+\sqrt3)(2+\sqrt3)`

Finally, just expand the product.

`(5+\sqrt3)(2+\sqrt3)=10+7\sqrt3+(\sqrt3)^2=\boxed{13+7\sqrt3}`