Question

add and/or subtract the given.
$-2sqrt{27} - 7sqrt{108}$
\\(\circ\\) $36\sqrt{3}$
\\(\circ\\) $-36\sqrt{3}$
\\(\circ\\) $48\sqrt{3}$
\\(\circ\\) $-48\sqrt{3}$

Explanation:

Step1: Simplify each square root

Simplify \(\sqrt{27}\) and \(\sqrt{108}\). We know that \(27 = 9\times3\) and \(108 = 36\times3\). So, \(\sqrt{27}=\sqrt{9\times3}=\sqrt{9}\times\sqrt{3}=3\sqrt{3}\) and \(\sqrt{108}=\sqrt{36\times3}=\sqrt{36}\times\sqrt{3}=6\sqrt{3}\).

Step2: Substitute back into the expression

Substitute the simplified square roots into the original expression: \(-2\sqrt{27}-7\sqrt{108}=-2\times3\sqrt{3}-7\times6\sqrt{3}\).

Step3: Perform the multiplications

Calculate the multiplications: \(-2\times3\sqrt{3}=-6\sqrt{3}\) and \(-7\times6\sqrt{3}=-42\sqrt{3}\).

Step4: Combine like terms

Combine the two terms: \(-6\sqrt{3}-42\sqrt{3}=(-6 - 42)\sqrt{3}=-48\sqrt{3}\).

Answer:

\(-48\sqrt{3}\)