How do i do this surd equation? With explination please!!

express in its least complex form:

5 <2> +3 <8> + <18>

8 <3> +2 <12> - <48>

<245> + <363> +2 <12> - <80>

<_> = square root sign. I don't know how to type it on a keyboard :/

thanks heaps for your help, and please explain how to do it. I'm not sure if this is right but i did the second one...

8 <3> +2 <12> - <48>
8 <3> +2 <6x2> - <6x8>
8 <3> +2 <2> - <8>
that's as far as i've got but i don't think it's right. I don't understand how you find perfect squares for number like 3 that don't have a perfect square :P

5 <2> + 3 <8> + <18>
5 <2> + 3 <4x2> + <9x2>
5 <2> + 3 <4> <2> + <9> <2>
5 <2> + 3x2 <2> + 3 <2>
(5+6+3) <2>
14 <2>

I trust you can figure the rest out yourself. They're all done the same way. For comparison, the answers are:

#2: 8 <3>

#3: 3 <5> + 9 <3>

To type √, hold down Alt and type 251 on the keypad. If you don't have a PC, with a keypad, I'm not sure how to do it.

Just factor the numbers under the radical, and take out any squares:
8 = 4x2 so √8 = √4 x √0 = 2√2
18 = 9x2 so √18 = 3√2
So 5 <2> +3 <8> + <18> = 5 √2 + 2√2 + 3√2 = 10√2

This should work for all of them. Getting rid of the squares leaves you with radicals that you can add up.

No, what you did isn't right. Don't factor out 6. Factor out squares, like 4 and 16.

we generally say sqrt(2)

sqrt(8) = sqrt(4)*sqrt(2) = 2*sqrt(2)
sqrt(18) = sqrt(9)*sqrt(2) = 3*sqrt(2)
so the first is
5*sqrt(2) + 3*sqrt(8) * sqrt(18)
=5*sqrt(2) + 3*2*sqrt(2) + 3*sqrt(2)
= 5*sqrt(2) * 6*sqrt(2) + 3*sqrt(2)
= (5+6+3) * sqrt(2) = 14*sqrt(2)

sqrt(12) = sqrt(4)*sqrt(3) = 2*sqrt(3)
sqrt(48) = sqrt(16)*sqrt(3) = 4*sqrt(3)
so the second is
8*sqrt(3) + 2*2*sqrt(3) - 4*sqrt(3) = (8+4-4) sqrt(3) = 8*sqrt(3)

sqrt(245) = sqrt(49)*sqrt(5) = 7*sqrt(5)
sqrt(363) = sqrt(121) * sqrt(3) = 11*sqrt(3)
sqrt(12) as above
sqrt(80) = sqrt(16) * sqrt(5) = 4 * sqrt(5)
so the third one is
7*sqrt(5) + 11*sqrt(3) + 2*2*sqrt(3) - 4*sqrt(5) = 15*sqrt(3) + 3*sqrt(5)

Either you need to ge all the < > the same 8(3)^(1/2) + 2 (12)^(1/2)= 8(3)^(1/2) +2(2)(3)^(1/2) = ect. and work them down using the rule EMDAS should do it