Question

\[\sqrt{3+2\sqrt{2}} - \sqrt{3-2\sqrt{2}}\]
How do you solve this without using a calculator? How the real problem looks like is under this.

Answer 1

\[\sqrt{3+2\sqrt{2}} - \sqrt{3-2\sqrt{2}}\]

Answer 2

multiply by the conjugate

Answer 3

how?

Answer 4

amistre do you know how?

Answer 5

all cause I typoed it in the beginning eh ... maybe

Answer 6

sqrt(3+2sqrt(2)) - sqrt(3-2sqrt(2)) = N ; ^2

3+2sqrt(2) + 3-2sqrt(2) -2sqrt((3+2sqrt(2))(3-2sqrt(2))) = N^2

6 -2sqrt[(3+2sqrt(2))(3-2sqrt(2))] = N^2

3 +2sqrt(2)
3 -2sqrt(2)
-----------
9 +6x
-6x -8
----------
9 -8 = 1


6 -2sqrt(1) = N^2

6 -2(1) = N^2

6 - 2 = N^2 = 4

N = +- 2 ; but in this case its gonna be 2

Answer 7

did you delete the other one? and the only thing i dont understand is going from steps 1 to 2

Answer 8

well, i started out by making it equal some number "N" and then tried to solve for N

the problem is that I squared each side and that has a tendency to bring in extra answers that dont apply

Answer 9

ohh okay. because i know the answer is two but i didnt know how to prove it

Answer 10

we can sift out the +- part with a bit of logic:

sqrt(4+2) - sqrt(4-2) is the same set up

sqrt(6) - sqrt(2)

sqrt(6) is larger than sqrt(2) so itll be a positive result

Answer 11

ok thanks!! and do you know how to solve\[\sqrt{2}+\sqrt{6} / \sqrt{2+\sqrt{3}}\]
and the square root after the divisor is actually under the the first part but i dont know how to show it on here

Answer 12

\frac{top}{bottom}

\[\frac{top}{bottom}\]

Answer 13

id just equate it to some unknown number N again and see what I could do to persuade it thru algebra

Answer 14

what does this say that you typed on the third line??

6 -2sqrt[(3+2sqrt(2))(3-2sqrt(2))] = N^2

Answer 15

where did you get 3 +2sqrt(2)
3 -2sqrt(2)
-----------
9 +6x
-6x -8
----------
9 -8 = 1

from??