Question

How do you evaluate `(6+ \sqrt { 7} ) ( 4- \sqrt { 7} )`?

Answer 1

You can use the F.O.I.L. method but that only applies to binomials (such as these). A more general method is to write each term of the first factor as a multiplier of the second factor.

Explanation:

Write each term of the first factor as a multiplier of the second factor:

`(6+ sqrt7) (4-sqrt 7) = 6(4-sqrt7) + sqrt7(4-sqrt7)`

Use the distributive property on both terms of the right side:

`(6+ sqrt7) (4-sqrt 7) = 24-6sqrt7 + 4sqrt7-sqrt7sqrt7`

The last term becomes -7:

`(6+ sqrt7) (4-sqrt 7) = 24-6sqrt7 + 4sqrt7-7`

Combine like terms:

`(6+ sqrt7) (4-sqrt 7) = 17-2sqrt7`