Question

simplify \\(\sqrt{3}(\sqrt{72} - 3\sqrt{2})\\). the simplified expression is \\(\square\\).

Explanation:

Step1: Simplify $\sqrt{72}$

We know that $72 = 36\times2$, so $\sqrt{72}=\sqrt{36\times2}=\sqrt{36}\times\sqrt{2}=6\sqrt{2}$.

Step2: Substitute back into the expression

The original expression $\sqrt{3}(\sqrt{72}-3\sqrt{2})$ becomes $\sqrt{3}(6\sqrt{2}-3\sqrt{2})$.

Step3: Combine like terms inside the parentheses

$6\sqrt{2}-3\sqrt{2} = 3\sqrt{2}$.

Step4: Multiply $\sqrt{3}$ and $3\sqrt{2}$

Using the property $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$, we get $\sqrt{3}\times3\sqrt{2}=3\sqrt{6}$.

Answer:

$3\sqrt{6}$