How do I simplify: 1 divided by (4 + square root of 3)?

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  • 3 years ago
    Favorite Answer

    = 1/(4 + √3) → when the denominator is like (a + √b), you multiply it by (a - √b), and you multiply the top too of course

    = [1 * (4 - √3)] / [(4 + √3).(4 - √3)]

    = (4 - √3) / [16 - 4√3 + 4√3 - 3]

    = (4 - √3) / [16 - 3]

    = (4 - √3)/13 ← no term with √ at the denominator

  • 3 years ago

    1/[4+sqr(3)]

    =

    1[4-sqr(3)]/(16-3)

    (multiply both the numerator

    & the denominator with

    4-sqr(3))

    =

    [4-sqr(3)]/13

  • Philip
    Lv 6
    3 years ago

    1/(4+rt3) = (4-rt3)/[(4-rt3)(4+rt3)] = (4-rt3)/(16-3) = (4-rt3)/13.

  • 3 years ago

    1 / (4 + square root 3) =

    1 / (4 + 1.73205) =

    1 / 5.73205 =

    0.174457654765747.

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  • Como
    Lv 7
    3 years ago

    4 - √3

    ------------------------

    [ 4 + √3 ] [4 - √3 ]

    4 - √3

    ----------

    13

  • 3 years ago

    1 / (4 + square root of 3)

    = (4 - square root of 3) / 13

  • 3 years ago

    1 / (4 +√3)

    Multiply top and bottom by 4 - √3

    (4 - √3) / (16 -3)

    (4 - √3) / 13

  • 3 years ago

    Rationalize the denominator by multiplying by its conjugate.

    1 / (4 + sqrt(3))

    = (4 - sqrt(3)) / (4 + sqrt(3))(4 - sqrt(3))

    = (4 - sqrt(3)) / (16 - 3)

    = (4 - sqrt(3)) / 13. Final.

  • 3 years ago

    = 1/(4 + sqrt(3))

    = 1/(4 + sqrt(3)) * (4 - sqrt(3))/4 -sqrt(3))

    =(4 -sqrt(3))/ ((4+sqrt(3))(4-sqrt(3)))

    = (4-sqrt(3)) /(4^2 - (sqrt(3))^2)

    = (4 - sqrt(3)) /(16 - 3)

    = (4 - sqrt(3)/13

  • 3 years ago

    It's already in simplest terms, but if you mean to clear the denominator, multiply top and bottom by the conjugate of the denominator. The conjugate is the same thing that is already on the bottom, but with the sign changed for the square root part. So multiply top and bottom by (4 - sqrt(3)). The bottom will multiply out into an integer.

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