Question

Which choice is equivalent to the expression below? VG+ 18+ 35-342

Answer 1

Answer:

D. 3√3 + √6

Explanation:

We have to simply the following expression.

$\sqrt[]{6}+\sqrt[]{18}+3\sqrt[]{3}-3\sqrt[]{2}$

The expression contains four terms, one of which (√18) can be further simplified.

Now we can write √18 as

$\sqrt[]{18}=\sqrt[]{2\cdot9}$$=\sqrt[]{9}\cdot\sqrt[]{2}$

since √9 = 3, the above becomes

$3\sqrt[]{2}$

Hence, our original expression becomes

$\begin{gathered} \sqrt[]{6}+\sqrt[]{18}+3\sqrt[]{3}-3\sqrt[]{2} \\ \Rightarrow\sqrt[]{6}+3\sqrt[]{2}+3\sqrt[]{3}-3\sqrt[]{2} \end{gathered}$

Now there are two 3√2 terms in the above expression, one negative and one positive. They cancel each other to give

$\begin{gathered} \sqrt[]{6}+3\sqrt[]{2}+3\sqrt[]{3}-3\sqrt[]{2} \\ \Rightarrow\boxed{\sqrt[]{6}+3\sqrt[]{3}} \end{gathered}$

Hence, our original expression √6 + √18 + 3√2 - 3√2 is equivalent to

$\sqrt[]{6}+3\sqrt[]{3}$

Now looking at the answer choices we see that our expression matches choice D.

Therefore, choice D is the correct answer!