• Apr 26th 2007, 05:05 PM
mathproffesor543
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
• Apr 26th 2007, 05:39 PM
smoothi963
square root(3+2sqroot2)- squareroot( 3-2sqrroot2)

Im not sure i understand that.

do you mean

square root(3+2sqroot2) MINUS the same thing?
• Apr 26th 2007, 05:53 PM
ThePerfectHacker
Quote:

Originally Posted by mathproffesor543
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.
• Apr 26th 2007, 07:43 PM
Soroban
Hello, mathproffesor!

Quote:

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)² . and . 3 - 2√2 .= .(√2 - 1)²

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

• Apr 26th 2007, 07:47 PM
Jhevon
Quote:

Originally Posted by Soroban
Hello, mathproffesor!

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

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

That's nice. How did you see that?
• Apr 27th 2007, 01:45 PM
Soroban
Hello, Jhevon!

Quote:

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)²

Just one more thing to watch for . . .