Question

simplify $(sqrt{3} + sqrt{48})(sqrt{20} - sqrt{5})$. the simplified expression is \boxed{}.

Explanation:

Step1: Simplify radicals

Simplify $\sqrt{48}$ and $\sqrt{20}$:
$\sqrt{48}=\sqrt{16\times3}=4\sqrt{3}$, $\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}$
So the expression becomes $(\sqrt{3} + 4\sqrt{3})(2\sqrt{5} - \sqrt{5})$

Step2: Combine like terms

Combine terms inside parentheses:
$\sqrt{3}+4\sqrt{3}=5\sqrt{3}$, $2\sqrt{5}-\sqrt{5}=\sqrt{5}$
Now the expression is $5\sqrt{3}\times\sqrt{5}$

Step3: Multiply radicals

Multiply the radicals:
$5\sqrt{3\times5}=5\sqrt{15}$

Answer:

$5\sqrt{15}$