Question

simplify ( 3sqrt{18} )

Explanation:

Step1: Factor the radicand

Factor 18 into $9\times2$, so $\sqrt{18}=\sqrt{9\times2}$.

Step2: Use square - root property

Using the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a\geq0,b\geq0$), we have $\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}$. Since $\sqrt{9} = 3$, then $\sqrt{18}=3\sqrt{2}$.

Step3: Multiply by the coefficient

We have $3\sqrt{18}=3\times(3\sqrt{2})$.

Step4: Calculate the product

$3\times3\sqrt{2}=9\sqrt{2}$.

Answer:

$9\sqrt{2}$