Multiply and Divide Radicals Quick Check

Question

1 of 51 of 5 Items
Question
Multiply (7–√) (−2–√)
. Give an exact answer.(1 point)
Responses

5–√
start root 5 end root

−14−−√
negative start root 14 end root

−72–√
negative 7 start root 2 end root

14−−√
start root 14 end root

Answer 1

To multiply the expression \((7 - \sqrt{2})(-2 - \sqrt{2})\), we use the distributive property (FOIL method).

1. First: Multiply the first terms: \[ 7 \cdot -2 = -14 \]

2. Outer: Multiply the outer terms: \[ 7 \cdot -\sqrt{2} = -7\sqrt{2} \]

3. Inner: Multiply the inner terms: \[ -\sqrt{2} \cdot -2 = 2\sqrt{2} \]

4. Last: Multiply the last terms: \[ -\sqrt{2} \cdot -\sqrt{2} = 2 \]

Now, combine all these results: \[ -14 - 7\sqrt{2} + 2\sqrt{2} + 2 \]

Combine like terms: \[ (-14 + 2) + (-7\sqrt{2} + 2\sqrt{2}) = -12 - 5\sqrt{2} \]

So, the final result is: \[ \boxed{-12 - 5\sqrt{2}} \]

If you had given possible options for responses that came in your question, please provide them for us to narrow down that answer. Based on the options you provided and calculations above, none of them seem to correspond, which suggests that there might be a misunderstanding with the formulation of multiplication or any error.