Question

What is the product of the radical expression?

(7 _sqrt7)(_6 +sqrt7)

a . _49 _ 42 sqrt7
b . _49 + 13 sqrt7
c . _35 _ 42 sqrt7
d . _6 + sqrt7

Answer 1

option (b) is correct

The product of
`(7-√(7) )` and
`(-6+√(7) )` is
`-49+13√(7)`

Explanation:

Given radicals
`(7-√(7) )` and
`(-6+√(7) )`

WE have to find the product of two given radicals

Consider
`\left(7-√(7)\:\right)\left(-6+√(7)\:\right)`

Using property of algebra,

`\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd` , We have ,

`=7\left(-6\right)+7√(7)+\left(-√(7)\right)\left(-6\right)+\left(-√(7)\right)√(7)`

Simplifying further , we get,

`=-7\cdot \:6+7√(7)+6√(7)-√(7)√(7)`

Adding similar terms , we get,

`=-49+13√(7)`

Thus, the product of
`(7-√(7) )` and
`(-6+√(7) )` is
`-49+13√(7)`

Thus, option (b) is correct

Answer 2

(7 _sqrt7)(_6 +sqrt7)= _49 + 13 sqrt7