Question

question
express in simplest radical form.
\\( 3\sqrt{150} + 3\sqrt{6} \\)

Explanation:

Step1: Simplify $\sqrt{150}$

Factor 150: $150 = 25\times6$. Then $\sqrt{150}=\sqrt{25\times6}=\sqrt{25}\times\sqrt{6}=5\sqrt{6}$ (since $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ for $a\geq0,b\geq0$ and $\sqrt{25}=5$).

Step2: Substitute back into the first term

The first term is $3\sqrt{150}$, so substitute $\sqrt{150}=5\sqrt{6}$: $3\times5\sqrt{6}=15\sqrt{6}$.

Step3: Combine like terms

Now the expression is $15\sqrt{6}+3\sqrt{6}$. Since both terms have $\sqrt{6}$, we can factor out $\sqrt{6}$: $(15 + 3)\sqrt{6}=18\sqrt{6}$.

Answer:

$18\sqrt{6}$