Question

How would the fraction71-√√√5using difference of squares?OA. 7-7√56OB. 7+7√56O c. 7+7√5OD. -7+7√5← PREVIOUSbe rewritten if its denominator is rationalizedSUBMIT

Answer 1

`D)-(7+7√(5)))/(4)`

1) Examining that ratio, we can perform the following:

`\begin{gathered} (7)/(1-√(5)) \\ \\ (7\left(1+√(5)\right))/(\left(1-√(5)\right)\left(1+√(5)\right)) \\ \\ (7+7√(5))/(1^2-(√(5))^2) \\ \\ (7(1+√(5)))/(-4) \\ \\ -(7(1+√(5)))/(4) \end{gathered}`

2) Note that when we multiply that ratio by their conjugates, that yields a difference between two squares. Note that on the top, there is the expanded version of this expression.

Thus, the answer is D