To simplify @12, you would find out multiplies out to get 12, so 3 x 2 x 2 works best:

@ 12

= @ (3 x 2 x 2) <-- Note that 2 x 2 is 4, which is a square, so the square root of 4 is 2. = @ (4 x 3) = 2 @ 3. You cannot simplify @ 6 because 2 and 3 multiplies out to 6, and none of those factors can have an integer square root result. 2 @ 2 is already simplified. Your question is pretty vague. Are you multiplying these radicals? If you multiply @ 12 by @ 6, you would multiply the numbers within the square roots. You would then get @ 72. 8 x 9 multiplies to get 72 (and 4 and 2 multiply to get 8). So: @ 12 x @ 6 = @(12 x 6) = @ 72 = @(4 x 9 x 2) = 2 x 3 @ 2 = 6 @ 2 I hope this helps. --- Ok. I saw your updated question. Which part of simplifying radicals do you not get? (Feel free to update your question ... I'll check back) If you do need more help fast, you can go to your math teacher and ask him/her to help you, as it is much easier to teach one-on-one than on the computer.

Example: Square root of 40

We want to break 40 up into 2 numbers, one of which is a perfect square. (Perfect squares: 4, 9, 16, 25, 36, 49, 64, 81…)

so 40 can be 4 x 10

We get the square root of 4 times the square root of 10

the square root of 4 = 2

The simplified answer is 2 times the square root of 10

(in your words: 2@10)

If you’re simplifying sqrt(12), then you break it into roots and factor out as much as possible.

sqrt(12) = sqrt(4) * sqrt(3) = 2 * sqrt(3)

if you’re trying to find the answer to all of them multiplied together

then use 2 *sqrt(3) for 12 from above, and multiply the rest

4 * sqrt(12), then factor again, 8 * sqrt(3)

to see if you got your answer right square the left numebr and multiply it by the one in the box to get the original number

Do you mean

sqrt(12 sqrt(62 sqrt(2)))?

…Okay, mebbe that didn’t help. (I’m pretty I made it worse, sorry!)

Feel free to message me for help. (And perhaps make a picture on Paint and host on tinypic.com so it’s easier for us to understand.)