Question

Shortern this expression pls​

Answer 1

`c =(8)/(3)`

Explanation:

Given

`c = \sqrt{(4 + \sqrt 7)/(4 - \sqrt 7)} + \sqrt{(4 - \sqrt 7)/(4 + \sqrt 7)}`

Required

Shorten

We have:

`c = \sqrt{(4 + \sqrt 7)/(4 - \sqrt 7)} + \sqrt{(4 - \sqrt 7)/(4 + \sqrt 7)}`

Rationalize

`c = \sqrt{(4 + \sqrt 7)/(4 - \sqrt 7) * (4 + \sqrt 7)/(4 + \sqrt 7)} + \sqrt{(4 - \sqrt 7)/(4 + \sqrt 7)*(4 - \sqrt 7)/(4 - \sqrt 7)}`

Expand

`c = \sqrt{((4 + \sqrt 7)^2)/(4^2 - (\sqrt 7)^2)} + \sqrt{((4 - \sqrt 7)^2)/(4^2 - (\sqrt 7)^2)`

`c = \sqrt{((4 + \sqrt 7)^2)/(16 - 7)} + \sqrt{((4 - \sqrt 7)^2)/(16 - 7)`

`c = \sqrt{((4 + \sqrt 7)^2)/(9)} + \sqrt{((4 - \sqrt 7)^2)/(9)`

Take positive square roots

`c =(4 + \sqrt 7)/(3) + (4 - \sqrt 7)/(3)`

Take LCM

`c =(4 + \sqrt 7 + 4 - \sqrt 7)/(3)`

Collect like terms

`c =(4 + 4+ \sqrt 7 - \sqrt 7)/(3)`

`c =(8)/(3)`