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math

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Simplify the radical expression by rationalizing the denominator:

2(square root)108 / (square root) 180y

Please show me how to set up and how to solve

  • math -

    I'm going to assume your problem is this:

    2√108
    -----
    √180y

    Multiply both the top and bottom by the equivalent of 1.

    2√108.....√180y
    ----- X -------
    √180y.....√180y

    Now we have:

    2√108 * √180y
    -------------
    180y

    Try to find factors to reduce this radical expression:

    2√(2*2*3*3*3) * √(2*2*3*3*5)
    ----------------------------
    180y

    Now we have:

    2*2*3*√3 * 2*3*√5
    -----------------
    180y

    12√3 * 6√5
    ----------
    180y

    72√15
    ------
    180y

    Reduces to:

    2√15
    ----
    5

    And there you have it!

  • Correction -

    Oops! Forgot to carry the y along in both the numerator and denominator.

    From this point on, here's how it works out:

    Try to find factors to reduce this radical expression:

    2√(2*2*3*3*3) * √(2*2*3*3*5*y)
    ----------------------------
    180y

    Now we have:

    2*2*3*√3 * 2*3*√5y
    -----------------
    180y

    12√3 * 6√5y
    ----------
    180y

    72√15y
    ------
    180y

    Reduces to:

    2√15y
    ----
    5y


    Sorry for any confusion!

  • math -

    THANK YOU MY GOD YOU SAVED MY LIFE

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