How do you FOIL #(√5 + √2) (√5 - √2)#?

Question

Eli Assouline · Accepted Answer

#5-2=3# #(sqrt(5)+sqrt(2))(sqrt(5)-sqrt(2))=# #=(sqrt(5)sqrt(5))cancel(-(sqrt(5)sqrt(2)))+cancel((sqrt(2)sqrt(5)))-(sqrt(2)sqrt(2))=# #=5-2=3#

Eva Adamson · Answer

undefined To FOIL (√5 + √2) (√5 - √2), follow the FOIL method:
First, multiply the first terms: (√5)(√5) = 5
Next, multiply the outer terms: (√5)(-√2) = -√10
Then, multiply the inner terms: (√2)(√5) = √10
Finally, multiply the last terms: (√2)(-√2) = -2
Combine the results: 5 - √10 + √10 - 2
Simplify: 5 - 2 = 3

HIX Tutor · Answer

undefined FOIL is a way to multiply two binomials. Here's how to do it step by step:

1. **First:** Multiply the first terms.
   - $ \sqrt{5} \times \sqrt{5} = 5 $

2. **Outside:** Multiply the outside terms.
   - $ \sqrt{5} \times -\sqrt{2} = -\sqrt{10} $

3. **Inside:** Multiply the inside terms.
   - $ \sqrt{2} \times \sqrt{5} = \sqrt{10} $

4. **Last:** Multiply the last terms.
   - $ \sqrt{2} \times -\sqrt{2} = -2 $

Now, put it all together:
- Start with the first result: $ 5 $
- Add the outside and inside results: $ -\sqrt{10} + \sqrt{10} $ (these cancel out)
- Add the last result: $ -2 $

So, the final answer is:
$ 5 - 2 = 3 $

The answer is **3**!