Question

express in simplest radical form.

$-5\sqrt{75} - \sqrt{147}$

answer
attempt 1 out of 2

submit answer
$\sqrt{}$

Explanation:

Step1: Simplify \(\sqrt{75}\)

Factor 75: \(75 = 25\times3\), so \(\sqrt{75}=\sqrt{25\times3}=\sqrt{25}\times\sqrt{3}=5\sqrt{3}\)

Step2: Simplify \(\sqrt{147}\)

Factor 147: \(147 = 49\times3\), so \(\sqrt{147}=\sqrt{49\times3}=\sqrt{49}\times\sqrt{3}=7\sqrt{3}\)

Step3: Substitute back into the original expression

\(-5\sqrt{75}-\sqrt{147}=-5\times5\sqrt{3}-7\sqrt{3}=-25\sqrt{3}-7\sqrt{3}\)

Step4: Combine like terms

\(-25\sqrt{3}-7\sqrt{3}=(-25 - 7)\sqrt{3}=-32\sqrt{3}\)

Answer:

\(-32\sqrt{3}\)