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

Please explain

  • Algebra -

    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

  • Algebra -

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

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