Question

1. simplify the expression \\(\sqrt{288} - \sqrt{18}\\).

Explanation:

Step1: Simplify $\sqrt{288}$

We can factor 288 as $144\times2$. Since $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (for $a\geq0, b\geq0$), we have $\sqrt{288}=\sqrt{144\times2}=\sqrt{144}\times\sqrt{2}=12\sqrt{2}$.

Step2: Simplify $\sqrt{18}$

Factor 18 as $9\times2$. Using the same square - root property, $\sqrt{18}=\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}=3\sqrt{2}$.

Step3: Subtract the two simplified radicals

Now we substitute the simplified forms back into the original expression: $\sqrt{288}-\sqrt{18}=12\sqrt{2}-3\sqrt{2}$. Since the terms have the same radical part ($\sqrt{2}$), we can combine like terms. Using the distributive property $ac - bc=(a - b)c$, here $a = 12$, $b = 3$, and $c=\sqrt{2}$, so $12\sqrt{2}-3\sqrt{2}=(12 - 3)\sqrt{2}=9\sqrt{2}$.

Answer:

$9\sqrt{2}$