Question

simplify the following

Answer 1

Answer:

$-20\sqrt{3}-5\sqrt{2}$

Step-by-step explanation:

Given expression:

$4 \sqrt{12}-\sqrt{50}-7\sqrt{48}$

Rewrite 12 as 4 · 3  and 50 as 25 · 2 and 48 as 16 · 3 :

$=4 \sqrt{4 \cdot 3}-\sqrt{25 \cdot 2}-7\sqrt{16 \cdot 3}$

$\textsf{Apply radical rule} \quad \sqrt{a \cdot b}=\sqrt{a}\sqrt{b} :$

$=4 \sqrt{4}\sqrt{3}-\sqrt{25}\sqrt{2}-7\sqrt{16}\sqrt{3}$

As $\sqrt{4}=2$ and $\sqrt{25}=5$ and $\sqrt{16}=4$ then:

$=4 \cdot 2 \sqrt{3}-5\sqrt{2}-7 \cdot 4\sqrt{3}$

Simplify:

$=8\sqrt{3}-5\sqrt{2}-28\sqrt{3}$

Collect like terms:

$=8\sqrt{3}-28\sqrt{3}-5\sqrt{2}$

Combine like terms:

$=-20\sqrt{3}-5\sqrt{2}$