Question

Question
What is the product of the following expression in simplest radical form?

218−−√⋅67–√
2
18
⋅
6
7


(1 point)

Answer 1

Interpret the expression as (√218·√67)/(√2·√18·√6·√7).

Simplify:
√218 = √2·√109, so cancel √2:
(√109·√67)/(√18·√6·√7) = √7303/(√18·√6·√7).

Compute √18·√6·√7 = √(18·6·7) = √(756) = √(36·21) = 6√21.

Thus the expression equals √7303/(6√21). Rationalizing the denominator gives
(√7303·√21)/(6·21) = √153363/126.

So the simplest radical form is √153363/126 (equivalently √7303/(6√21)).