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Math Help - [SOLVED] Nested Radical

  1. #1
    mathproffesor543
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    [SOLVED] Nested Radical

    cant figure this problem out for the life of me.

    USe your calculator to find teh value of the expression
    square root(3+2sqroot2)- squareroot( 3-2sqrroot2)

    Show algebracially that the gien expression is indeed the calculated value.


    The calculated value is 2, i just need to show how i got it. THanks
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  2. #2
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    square root(3+2sqroot2)- squareroot( 3-2sqrroot2)


    Im not sure i understand that.

    do you mean

    square root(3+2sqroot2) MINUS the same thing?
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  3. #3
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    Quote Originally Posted by mathproffesor543 View Post
    cant figure this problem out for the life of me.

    USe your calculator to find teh value of the expression
    square root(3+2sqroot2)- squareroot( 3-2sqrroot2)

    Show algebracially that the gien expression is indeed the calculated value.


    The calculated value is 2, i just need to show how i got it. THanks
    If they are the same then their squares are the same.
    Square both sides and see what you get.
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  4. #4
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    Hello, mathproffesor!

    Use your calculator to find the value of:
    . . . _______ . . _______
    . . √3 + 2√2 - √3 - 2√2 . . . (Answer: 2)

    Show algebracially that the given expression is indeed the calculated value.
    . . . . . . . . . . . . . ._ . - . . _ . . . - . . . - . . . . . ._ . - . - _
    Note that: . 3 + 2√2 .= .(√2 + 1) . and . 3 - 2√2 .= .(√2 - 1)

    . . . . . . . . . . . ________ - . ________ . . . . . _ . . - . . . _
    So we have: . √(√2 + 1) - √(√2 - 1) . = . (√2 + 1) - (√2 - 1) . = . 2

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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, mathproffesor!

    . . . . . . . . . . . . . ._ . - . . _ . . . - . . . - . . . . . ._ . - . - _
    Note that: . 3 + 2√2 .= .(√2 + 1) . and . 3 - 2√2 .= .(√2 - 1)

    . . . . . . . . . . . ________ - . ________ . . . . . _ . . - . . . _
    So we have: . √(√2 + 1) - √(√2 - 1) . = . (√2 + 1) - (√2 - 1) . = . 2

    That's nice. How did you see that?
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  6. #6
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    Hello, Jhevon!

    How did you see that?
    I really didn't "see" it, but . . .

    Experience has taught me that: if there is a radical expression under a square root,
    . . it might be a perfect square . . . so I am suspicious, you see.

    . . . - . . . . . . - . . . . . . . . . _______
    One of the strangest was: .√5 + 2√6
    . . . . . . . . . . . . . . . . . . ._ . - - . _ - - ._
    It turned out that: .5 + 2√6 .= .(√2 + √3)

    Just one more thing to watch for . . .

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