Question

simplify.
$9\sqrt{18}$

Explanation:

Step1: Factor the radicand

Factor 18 into a product of a perfect square and another number: $18 = 9\times2$. So, $\sqrt{18}=\sqrt{9\times2}$.

Step2: Use the square - root property

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

Step3: Multiply by the coefficient outside the radical

We have $9\sqrt{18}=9\times3\sqrt{2}$.

Step4: Calculate the product of the coefficients

$9\times3 = 27$, so $9\sqrt{18}=27\sqrt{2}$.

Answer:

$27\sqrt{2}$