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

Upon simplifying the given expression by combining like terms and simplifying radicals, the expression √6 + √18 + 3√3 - 3√2 comes down to 3√3 + √6, which corresponds to choice D.

Step-by-step explanation:

The expression √6 + √18 + 3√3 - 3√2 requires simplification by combining like terms and simplifying any radical expressions.

Firstly, look for like radical terms. The square root of 18 can be simplified to 3√2, because 18 is 9*2 and the square root of 9 is 3.

Now we rewrite the expression with the simplified term: √6 + 3√2 + 3√3 - 3√2

Notice that 3√2 and -3√2 are like terms and will cancel each other out. The expression now simplifies further to: √6 + 3√3

There are no more like radical terms to combine, so this is the simplified expression. Considering the answer choices given, the equivalent expression is 3√3 + √6.

Therefore, the correct answer is D. 3√3 + √6.