Question

Rationalize the denominators.

5/(3+sqrt(5))

Answer 1

5 / ( 3 + √ 5 )

Multiply both sides by ( 3 - √ 5 )

5 ( 3 - √ 5 ) / [ ( 3 + √ 5 ) ( 3 - √ 5 ) ] =

5 ( 3 - √ 5 ) / ( 3 ∙ 3 + 3 ∙ √ 5 - √ 5 ∙ 3 - √ 5 ∙ √ 5 ) =

5 ( 3 - √ 5 ) / ( 9 + 3 √ 5 - 3 √ 5 - 5 ) =

5 ( 3 - √ 5 ) / ( 9 - 5 ) =

5 ( 3 - √ 5 ) / 4 =

5 / 4 ( 3 - √ 5 )

5 / ( 3 + √ 5 ) = 5 / 4 ( 3 - √ 5 )