Question

What is the simplified version of ula1" title="(2\sqrt{5}+3)(\sqrt{5}-1)" alt="(2\sqrt{5}+3)(\sqrt{5}-1)" align="absmiddle" class="latex-formula">

Answer 1

ANSWER

EXPLANATION

We want to simplify:

$(2\sqrt{5}+3)(\sqrt{5}-1)$

Recall the distributive property;

(a+b)(c+d)=a(c+d)+b(c+d)

We apply this property to get,

$2\sqrt{5}(\sqrt{5}-1) + 3(\sqrt{5}-1)$

We expand to get,

$2 \times 5-2 \sqrt{5} + 3\sqrt{5}-3$

This simplifies to,

$10 + \sqrt{5}-3$

The simplest form of the given expression is:

$7 + \sqrt{5}$