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Math Help - square root of an even power

  1. #1
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    square root of an even power

    sqrt(4x^2 + 9x^4) = sqrt(x^2*(4+9x^2)) = |x|*sqrt(4+9x^2)) is that absolute value sign always necessary when you take out an x squared from under the radical? what if it is something like

    sqrt(4*t^2*sin^2(t^2)+4*t^2*cos^2(t^2)))
    does that turn out to be |2t|*sqrt(sin^2(t^2)+cos^2(t^2))
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  2. #2
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    Quote Originally Posted by zintore View Post
    sqrt(4x^2 + 9x^4) = sqrt(x^2*(4+9x^2)) = |x|*sqrt(4+9x^2)) is that absolute value sign always necessary when you take out an x squared from under the radical? what if it is something like

    sqrt(4*t^2*sin^2(t^2)+4*t^2*cos^2(t^2)))
    does that turn out to be |2t|*sqrt(sin^2(t^2)+cos^2(t^2))
    Yes you need to take absolute value. Because otherwise it would mean sqrt[ (-1)^2 ] = -1 which is wrong.
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