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Math Help - Basic Square Root Question

  1. #1
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    Basic Square Root Question

    I was reading an article on Purplemath about simplifying the square root terms. For instance in \sqrt{144} they instruct users to break down as a product and simply from there  \sqrt{144}=\sqrt{9*16}=3*4=12.

    However what if you used a different pair of factors? Such as \sqrt{144}=\sqrt{3*48}? I understand once you get a perfect square you can remove it from under the radicand, but I attempted this problem and could not figure it out with the pair of factors I have. \sqrt{144}=\sqrt{3*48}=\sqrt{3}\sqrt{2x24}=\sqrt{3  }\sqrt{2}\sqrt{2x12} etc


    I understand that we could simply solve by
    knowing 12^2=144 but that defeats the purpose of this exercise.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by HenryJ View Post
    I was reading an article on Purplemath about simplifying the square root terms. For instance in \sqrt{144} they instruct users to break down as a product and simply from there  \sqrt{144}=\sqrt{9*16}=3*4=12.

    However what if you used a different pair of factors? Such as \sqrt{144}=\sqrt{3*48}? I understand once you get a perfect square you can remove it from under the radicand, but I attempted this problem and could not figure it out with the pair of factors I have. \sqrt{144}=\sqrt{3*48}=\sqrt{3}\sqrt{2x24}=\sqrt{3  }\sqrt{2}\sqrt{2x12} etc


    I understand that we could simply solve by
    knowing 12^2=144 but that defeats the purpose of this exercise.
    \sqrt{3}\sqrt{48}=\sqrt{3}\sqrt{3}\sqrt{16}=\sqrt{  3}\sqrt{3}\sqrt{4}\sqrt{4}=(\sqrt{3})^2(\sqrt{4})^  2
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  3. #3
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    Where did I go wrong?

    \sqrt{144}=\sqrt{3*48}=\sqrt{3}\sqrt{2*24}=\sqrt{3  }\sqrt{2}\sqrt{2*12}=\sqrt{3}\sqrt{2}\sqrt{2}\sqrt  {3*4} =(\sqrt{3})^2(\sqrt{2})^2*4=3*2*4=24
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  4. #4
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    Quote Originally Posted by HenryJ View Post
    Where did I go wrong?

    \sqrt{144}=\sqrt{3*48}=\sqrt{3}\sqrt{2*24}=\sqrt{3  }\sqrt{2}\sqrt{2*12}=\sqrt{3}\sqrt{2}\sqrt{2}\sqrt  {3*4} =(\sqrt{3})^2(\sqrt{2})^2*4=3*2*4=24
    You have mistaken \sqrt{4} for 4 in your 6th step.
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  5. #5
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    So I have thank you!
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  6. #6
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by HenryJ View Post
    So I have thank you!
    The bottom line:

    If you have factored properly, there will be no problems.
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