Question

What is the product of the radical expression? (7- sqr root 2)(8+ sqr root 2)

Answer 1

`(7 -√(2) )(8+ √(2) )\\ \\ =56 + 7 √(2)-8 √(2)-2 \\ \\=54- √(2)`

Answer 2

`54-√(2)`

Step-by-step explanation:

We have been given a radical expression
`(7-√(2)) (8+√(2))` and we are asked to find the product of our given expression.

Upon using FOIL method we will get,

`7(8+√(2))-√(2) (8+√(2) )`

Now let us simplify our radical expression.

`(56+7√(2))-(8√(2) +√(4) )`

`56+7√(2)-8√(2) -√(4)`

`56+7√(2)-8√(2) -2`

Now let us combine like terms.

`(56-2)+(7-8)√(2)`

`(54)+(-1)√(2)`

`54-√(2)`

Therefore, product of our radical expression is
`54-√(2)`.