Thread: [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

square root(3+2sqroot2)- squareroot( 3-2sqrroot2)


Im not sure i understand that.

do you mean

square root(3+2sqroot2) MINUS the same thing?

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.

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)² . and . 3 - 2√2 .= .(√2 - 1)²

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

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?

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)²

Just one more thing to watch for . . .