Question

Simplify:fraction numerator square root of 84 plus 8 over denominator 4 end fractionAnswer choices include:A. fraction numerator square root of 14 plus 4 over denominator 2 end fractionB. 2 square root of 21 plus 2C. 2 square root of 14 plus 2D. fraction numerator square root of 21 plus 4 over denominator 2 end fraction

Answer 1

`(4+21)/(2)`

1) Let's turn that from English to Math:

`(8+√(84))/(4)`

2) Note that we can rewrite that and then factor out the GCD to rewrite it as a product and simplify it as much as we can.

`\begin{gathered} (8+√(84))/(4) \\ (8+√(2^2\cdot\:3\cdot\:7))/(4) \\ (8+2√(21))/(4) \\ (2\left(4+√(21)\right))/(4) \\ (2\left(4+√(21)\right))/(2\cdot \:2) \\ (4+√(21))/(2) \end{gathered}`

Note that in the options the terms are flipped, but this is not a problem. So we can tell that the answer is: