Question

How do I solve for (2√5−√3)^2?

Answer 1

The answer is 23-4√15

Answer 2

`23-4√(15)`

Explanation:

So we want to simplify:

`(2\sqrt5-\sqrt3)^2`

Note that this is in the format:

`(a-b)^2`

And we know that this is the same as:

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

Let 2√5 be a and let √3 be b. Thus:

`(2\sqrt5-\sqrt3)^2\\=(2\sqrt5)^2-2(2\sqrt5)(\sqrt3)+(\sqrt3)^2`

Simplify:

`=(4(5))-4(\sqrt5)(\sqrt3)+(3)\\=20-4√(15)+3\\=23-4√(15)`

And this cannot be simplified any further.