simplify. 9\\sqrt{18}

Explanation:

Step1: Factorize 18

$18 = 9\times2$

Step2: Rewrite the square - root

$9\sqrt{18}=9\sqrt{9\times2}$

Step3: Use the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 9$, $b = 2$)

$9\sqrt{9\times2}=9\times\sqrt{9}\times\sqrt{2}$

Step4: Evaluate $\sqrt{9}$

Since $\sqrt{9}=3$, then $9\times\sqrt{9}\times\sqrt{2}=9\times3\times\sqrt{2}$

Step5: Calculate the product

$9\times3\times\sqrt{2}=27\sqrt{2}$

Answer:

$27\sqrt{2}$