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Math Help - Square Roots and other things to simplify

  1. #1
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    Square Roots and other things to simplify

    I've started accelerated geometry now, in 8th grade, and an algebra review packet is due. I really need help to remember how to do problems like -

    [square root of] 48rs^3


    [square root of]63 + [square root of]28 - [square root of]1/7



    3[square root of]5x
    ------------------- (over)
    5[square root of]6y



    x^2 + 2x + 1
    ----(over)
    3x
    -------------(all over)
    x+1
    ----(over)
    2x

    Sorry, I didn't know how to use the math tags. I hope you will be able to read it.

    Could someone please solve these and then show me how they did it?
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  2. #2
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    Quote Originally Posted by Harryhit4 View Post
    [square root of] 48rs^3
    Pull out all the square things.

    48 = 3*16 = 3*4^{2}

    s^{3} = s*s^{2}

    So, \sqrt{48rs^{3}} = 4|s|\sqrt{3rs}
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    Pull out all the square things.

    48 = 3*16 = 3*4^{2}

    s^{3} = s*s^{2}

    So, \sqrt{48rs^{3}} = 4|s|\sqrt{3rs}
    Thanks, can anyone else help me with the others?
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Harryhit4 View Post
    x^2 + 2x + 1
    ----(over)
    3x
    -------------(all over)
    x+1
    ----(over)
    2x
    The LCM of 3x and 2x is 6x, so you multiply the fraction by \frac{6x}{6x} = 1, which does not change the value.

    \frac{ \frac{x^2 + 2x + 1}{3x} }{ \frac{x + 1}{2x} }

    = \frac{ \frac{x^2 + 2x + 1}{3x} }{ \frac{x + 1}{2x} } \cdot \frac{6x}{6x};~x \neq 0

    = \frac{ \frac{x^2 + 2x + 1}{3x} \cdot 6x}{ \frac{x + 1}{2x} \cdot 6x};~x \neq 0

    = \frac{2(x^2 + 2x + 1)}{3(x + 1)};~x \neq 0

    Now do some factoring:
    = \frac{2(x + 1)^2}{3(x + 1)};~x \neq 0

    = \frac{2(x + 1)}{3};~x \neq -1,0

    -Dan
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