Question

Which choice is equivalent to the expression below?

√6 + √18 + 3√3 - 3√2

A. 5√3
B. 5√3 - 6
C. 2√3 - √24
D. 3√3 + √6

Answer 1

To simplify the expression √6 + √18 + 3√3 - 3√2, combine like terms to get 6√2.

Step-by-step explanation:

To simplify the expression √6 + √18 + 3√3 - 3√2, we can combine like terms.

We group the terms with square root of 6 and square root of 18, which can be simplified:

√6 + √18 = √2 * 3 + √2 * 9 = 3√2 + 3√2 = 6√2

Similarly, we group the terms with square root of 3 and square root of 2:

3√3 - 3√2 = 3√3 - 3√2 = 0

So the simplified expression is 6√2 + 0, which is equivalent to 6√2.

Notice that \(3\sqrt{2}<\/strong>) is added and subtracted, so they cancel each other out. After simplifying, the remaining terms are \(\sqrt{6} + 3\sqrt{3}<\/strong>). Therefore, the correct choice is equivalent to option D. 3\sqrt{3} + \sqrt{6}<\/strong>.