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Math Help - Sanity Check

  1. #1
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    Sanity Check

    My son has a question on a school paper which goes as follows

    Simplify

    \sqrt{\left ( 15p \right )^{2}-\left ( 9k \right )^{2}}

    Maybe I am losing it, but this does not seem like it can be simplified. If the minus was a times then ok, but not like this.
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  2. #2
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    Re: Sanity Check

    Quote Originally Posted by grillage View Post
    My son has a question on a school paper which goes as follows

    Simplify

    \sqrt{\left ( 15p \right )^{2}-\left ( 9k \right )^{2}}
    you can do one small thing

    \sqrt{\left ( 15p \right )^{2}-\left ( 9k \right )^{2}}

    \sqrt{3^2\cdot 25p^2 - 3^2\cdot 9k^2}

    3\sqrt{25p^2-9k^2}
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  3. #3
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    Re: Sanity Check

    Thanks, but I still suspect that they intended a multiplication.
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  4. #4
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    Re: Sanity Check

    you can factor it to become

    3\sqrt{(5p-3k)(5p+3k)}

    I don't know that I'd call that any simpler.
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  5. #5
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    Re: Sanity Check

    Hello, grillage!

    Sanity Check

    My son has a question on a school paper which goes as follows:

    Simplify: . \sqrt{\left ( 15p \right )^{2}-\left ( 9k \right )^{2}}

    Maybe I am losing it, but this does not seem like it can be simplified.
    If the minus was a times, then ok, but not like this.

    It can be simplifed as romsek suggested.

    Your son could invoke the Sanity Clause that excuses him from the problem.

    But, of course, there isn't any Sanity Clause.
    Thanks from sakonpure6
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