Question

simplify the expression: $3\sqrt{18} - 2\sqrt{2}$

Explanation:

Step1: Simplify $\sqrt{18}$

We know that $18 = 9\times2$, and $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (for $a\geq0,b\geq0$). So $\sqrt{18}=\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}=3\sqrt{2}$.

Step2: Substitute and simplify the expression

Substitute $\sqrt{18}=3\sqrt{2}$ into the original expression $3\sqrt{18}-2\sqrt{2}$, we get $3\times(3\sqrt{2})-2\sqrt{2}$.
First, calculate $3\times(3\sqrt{2}) = 9\sqrt{2}$. Then the expression becomes $9\sqrt{2}-2\sqrt{2}$.
Since $9\sqrt{2}$ and $2\sqrt{2}$ are like terms (they have the same radical part $\sqrt{2}$), we can subtract their coefficients: $(9 - 2)\sqrt{2}=7\sqrt{2}$.

Answer:

$7\sqrt{2}$