Question

How do I solve for (2√5−√3)^2?

Answer 1

The answer is 23-4√15

Answer 2

Answer:

$23-4\sqrt{15}$

Step-by-step 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:

$=(4(5))-4(\sqrt5)(\sqrt3)+(3)\\=20-4\sqrt{15}+3\\=23-4\sqrt{15}$

And this cannot be simplified any further.