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Math Help - Radicals Within Radical

  1. #1
    Super Member nycmath's Avatar
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    Radicals Within Radical

    Are these two quantities alike or not alike?
    Does one side agree with the other?

    sqrt(7) - sqrt{8-2sqrt(7)} = 1
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    Re: Radicals Within Radical

    transfer 1 to the left and the sqrt{8-...) to the right and then rise to power 2 and see what you get......it is easy
    you can do it yourself.
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    Super Member nycmath's Avatar
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    Re: Radicals Within Radical

    sqrt(7) - sqrt{8-2sqrt(7)} = 1

    One of the expressions contains a radical within another radical.

    sqrt{8-2sqrt(7)} = the square of 8 minus 2 times the square root of 7. All of this lies under one giant radical.

    You are saying to move one expression to the right and then square both sides.

    The original question is asking to show, to verify if both sides are equal. Does the left side equal 1?

    Does sqrt(7) - sqrt{8-2sqrt(7)} equal one?

    If I move one of the expressions to the right, it changes the value of 1 to (1-sqrt{7}). After squaring both sides, the two sides are not equal but this answer has nothing to do with the original request.

    Does the left side containing a radical 7 minus a giant radical containing a radical within a radical equal 1?

    Can you demonstrate just how "easy" this can be done without a calculator?
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  4. #4
    Forum Admin topsquark's Avatar
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    Re: Radicals Within Radical

    Quote Originally Posted by nycmath View Post
    sqrt(7) - sqrt{8-2sqrt(7)} = 1

    One of the expressions contains a radical within another radical.

    sqrt{8-2sqrt(7)} = the square of 8 minus 2 times the square root of 7. All of this lies under one giant radical.

    You are saying to move one expression to the right and then square both sides.

    The original question is asking to show, to verify if both sides are equal. Does the left side equal 1?

    Does sqrt(7) - sqrt{8-2sqrt(7)} equal one?

    If I move one of the expressions to the right, it changes the value of 1 to (1-sqrt{7}). After squaring both sides, the two sides are not equal but this answer has nothing to do with the original request.

    Does the left side containing a radical 7 minus a giant radical containing a radical within a radical equal 1?

    Can you demonstrate just how "easy" this can be done without a calculator?
    As I mentioned in the other thread with a similar problem, you want to get rid of that double square root. So isolate it:
    \sqrt{7} - \sqrt{8-2\sqrt{7}} = 1

    \sqrt{7} - 1 = \sqrt{8-2\sqrt{7}}

    Now square both sides and see what happens.

    -Dan

    PS Feel free to visit our LaTeX forum. It only looks like it's hard to use but you can actually pick it up fairly quickly.
    Last edited by topsquark; October 21st 2013 at 10:48 AM.
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    Super Member nycmath's Avatar
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    Re: Radicals Within Radical

    Thank you, Dan. I also received help from another user via private text. This is a radical equation problem beyond the typical high school question like sqrt{x+1} = 5. Solve for x.
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