Question

Rationalize the denominator: 5 /4-squareroot 5
(five over four minus square root five)

Please explain

Answer 1

since (a-b)(a+b) = a^2 - b^2,

(4-sqrt(5))(4+sqrt(5) = 16-5 = 11

so, multiply top and bottom by 4+sqrt(5) to get

5(4+sqrt(5))/11 = (20 + 5sqrt(5))/11

Answer 2

Thank you so much!! It really helped me understand!