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Math Help - What is wrong with these operations? My calculator produces a different answer

  1. #1
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    What is wrong with these operations? My calculator produces a different answer

    In this book I'm reading, there are three problems I'm having a hard time with.

    1. \sqrt{12}\times\sqrt{5}=\sqrt{60}=2\sqrt{15}

    When I enter \sqrt{12}\times\sqrt{5} on my TI-84+ and hit Enter, I get 7.745966692 instead.

    2. 3\sqrt{2}\times4\sqrt{8}=12\sqrt{16}=48

    When I enter 3\sqrt{2}\times4\sqrt{8} on my TI-84+ and hit Enter, I get 48, so that answer agrees with the book.

    3. 2\sqrt{10}\times6\sqrt{5}=12\sqrt{50}=60\sqrt{2}

    When I enter 2\sqrt{10}\times6\sqrt{5} on my TI-84+ and hit Enter, I get 84.85281374 instead.

    Can anybody explain why my answer is different and what the book's answer means?

    Roger
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  2. #2
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    Quote Originally Posted by jairtime View Post
    In this book I'm reading, there are three problems I'm having a hard time with.

    1. \sqrt{12}\times\sqrt{5}=\sqrt{60}=2\sqrt{15}

    When I enter \sqrt{12}\times\sqrt{5} on my TI-84+ and hit Enter, I get 7.745966692 instead.

    2. 3\sqrt{2}\times4\sqrt{8}=12\sqrt{16}=48

    When I enter 3\sqrt{2}\times4\sqrt{8} on my TI-84+ and hit Enter, I get 48, so that answer agrees with the book.

    3. 2\sqrt{10}\times6\sqrt{5}=12\sqrt{50}=60\sqrt{2}

    When I enter 2\sqrt{10}\times6\sqrt{5} on my TI-84+ and hit Enter, I get 84.85281374 instead.

    Can anybody explain why my answer is different and what the book's answer means?

    Roger
    Hello,

    your calculator is not able to handle symbols like \sqrt{\ \ }. It has a build-in function which returns an approximative value. For instance: If you type \sqrt{15} the calculator uses 3.872983346.. and as far as I'm informed the TI84 uses internally(?) 14 decimals and rounds a result down to maximal 12 decimals.

    So considering the abilities of your calculator all results are OK.

    If you take #1:

    1. \sqrt{12}\times\sqrt{5}=\sqrt{60}=\sqrt{4 \cdot 15} = 2\sqrt{15}

    This method is called calculating a root partially: A value is transformed into a product of a square and a non-square(?). You can calculate the square-root of the square. But your calculator isn't able to do these transformations.
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  3. #3
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    Thanks

    Thanks again, Earboth.

    It puts a smile on my face to know that it's the calculator. I'm glad you know the answers to my questions!

    I wonder if my new TI-89 Titanium can handle the problem.

    Talk with you soon!

    Roger
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  4. #4
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    The very inexpensive Casio fx 83ES will give answers in surd form.

    Of course where you're asked to do this in a test you won't be allowed to use a calculator, I'm guessing.
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