Question

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

Answer 1

D. 3√3 + √6

Step-by-step 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!