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Math Help - Prove that it is smaller than 6

  1. #1
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    Prove that it is smaller than 6

    Prove that Prove that it is smaller than 6-msp340419h1i98721f4618g000016f428dc98cfg230.gif.

    How do i prove this? thank you...
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Prove that it is smaller than 6

    A possibility is to take the square of both sides.
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Re: Prove that it is smaller than 6

    Quote Originally Posted by MichaelLight View Post
    Prove that Click image for larger version. 

Name:	MSP340419h1i98721f4618g000016f428dc98cfg230.gif 
Views:	29 
Size:	701 Bytes 
ID:	22141.

    How do i prove this? thank you...
    \sqrt{10}+2\sqrt{2}<6

    \Leftrightarrow 10+8+8\sqrt{5}<36 (Squaring both sides)

    \Leftrightarrow 8\sqrt{5}<18

    \Leftrightarrow 320<324 (Squaring both sides)

    which is true.
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  4. #4
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    Re: Prove that it is smaller than 6

    Quote Originally Posted by MichaelLight View Post
    Prove that Click image for larger version. 

Name:	MSP340419h1i98721f4618g000016f428dc98cfg230.gif 
Views:	29 
Size:	701 Bytes 
ID:	22141.

    How do i prove this? thank you...
    Suppose otherwise, then by assumption:

    \sqrt{10}+2\sqrt{2}\ge 6

    Now square both sides and follow the consequences to get a contradiction.

    CB
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  5. #5
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    Re: Prove that it is smaller than 6

    Quote Originally Posted by alexmahone View Post
    \sqrt{10}+2\sqrt{2}<6

    \Leftrightarrow 10+8+8\sqrt{5}<36 (Squaring both sides)

    \Leftrightarrow 8\sqrt{5}<18

    \Leftrightarrow 320<324 (Squaring both sides)

    which is true.
    Normally, one would NOT start a proof by assuming what you want to prove, as alexmahone does here. However, this is a perfectly valid "synthetic proof". Every step is invertible. A "standard" proof would be given by going from "320< 324" upward.
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