Question

adding / subtracting radical expressions
score: 4/8 penalty: none
question
express in simplest radical form.
$-sqrt{24} - sqrt{150}$
answer
submit answer

Explanation:

Step1: Simplify \(\sqrt{24}\)

Factor 24 into \(4\times6\), so \(\sqrt{24}=\sqrt{4\times6}\). Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we get \(\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}\). Thus, \(-\sqrt{24}=-2\sqrt{6}\).

Step2: Simplify \(\sqrt{150}\)

Factor 150 into \(25\times6\), so \(\sqrt{150}=\sqrt{25\times6}\). Using the same property, \(\sqrt{25\times6}=\sqrt{25}\times\sqrt{6}=5\sqrt{6}\).

Step3: Combine like terms

Now we have \(-\sqrt{24}-\sqrt{150}=-2\sqrt{6}-5\sqrt{6}\). Since the radicals are the same, we can combine the coefficients: \((-2 - 5)\sqrt{6}=-7\sqrt{6}\).

Answer:

\(-7\sqrt{6}\)