Question

What is the following product? (1√2+√6)(√6- √10)

Answer 1

To multiply these, we use the FOIL method (first, outside, inside, last). Also, 1√2 is equivalent to √2. It's just like saying 1x is the same x.

Multiplying the first values will give you:

√2 * √6 = √12 = √4*3 = √2*2*3 = 2√3

Multiplying the outside values will give you:

√2 * -√10 = -√20 = -√4*5 = -√2*2*5 = -2√5

Multiplying the inside values will give you:

√6 * √6 = √36 = 6

Multiplying the last values will give you:

√6 * -√10 = -√60 = -√4*15 = -2√15

Now you can combine all of the resulting values:

2√3 - 2√5 - 2√15 + 6

I believe this is the answer you're looking for.

Answer 2

Using the distributive property, this is
(√2)×(√6 -√10) +(√6)(√6 -√10)
= 2√3 - 2√5 +6 -2√15

The product is ...
6 +2√3 -2√5 -2√15

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When simplifying the product, it helps to realize that any factor of 4 inside the radical can be brought outside as a factor of √4 = 2.
(√2)(√6) = √12 = √(4*3) = 2√3
(√2)(√10) = √20 = √(4*5) = 2√5
(√6)(√10) = √60 = √(4*15) = 2√15