Question

add. write your answer in simplest form.
-√150 + 7√6

Explanation:

Step1: Simplify \(-\sqrt{150}\)

Factor 150: \(150 = 25\times6\), so \(\sqrt{150}=\sqrt{25\times6}\). By the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we get \(\sqrt{25\times6}=\sqrt{25}\times\sqrt{6}=5\sqrt{6}\). Thus, \(-\sqrt{150}=-5\sqrt{6}\).

Step2: Add the two radical terms

Now we have \(-5\sqrt{6}+7\sqrt{6}\). Since they are like radicals (same radicand \(\sqrt{6}\)), we combine the coefficients: \((-5 + 7)\sqrt{6}=2\sqrt{6}\).

Answer:

\(2\sqrt{6}\)