Expert: Jeff White - 10/12/2004

Question
The objective here is to simplify the sums and diffrences of radicals, you have to simplify and express and write each problem out step by step until you caome to the answer and i just dont understnd it at all.

1. 3 the square root box with 2 inside + 5 the square root box with 2 inside

2. 3 the square root box with 8 inside + 2 the square root box with 16 inside

3. The square root of 2 + the square root of 2 over 49

4. 3 the square root box with 2 inside + the square root of 50

5. ( the square root of 2-3)(the square root of 2+3)

6. ( the square root of 3- the square root of 5)(the square root of 3- the square root of 5)

7. This one you have to solve step by step

 The square root of x+5=8


Answer
You treat the radicals sort of like variables, meaning you can add like terms together.  So for example, on #1:
3*sqrt(2) + 5*sqrt(2) = 8*sqrt(2)

Also, if you factor what's under the radical, you can take the sqare root of any perfect square factors outside the radical, e.g., sqrt(8) = sqrt(4 * 2) = 2 * sqrt(2)

So #2 would be:
3*sqrt(8) + 2sqrt(16) =
3*2*sqrt(2) + 2*4 =
6*sqrt(2) + 8

On #3, use some parentheses or commas to clarify.  Is it sqrt(2) + sqrt(2), over 49...or sqrt(2), + sqrt(2)/49?

#4
3*sqrt(2) + sqrt(50) =
3*sqrt(2) + sqrt(2*25) =
3*sqrt(2) + 5*sqrt(2) =
8*sqrt(2)

#5
(sqrt(2) - 3)(sqrt(2) + 3)
Multiply these together using the FOIL method:
sqrt(2)*sqrt(2) + 3*sqrt(2) - 3*sqrt(2) - 9 =
2 - 9 = -7

#6
(sqrt(3) - sqrt(5))(sqrt(3) - sqrt(5)) =
3 - sqrt(15) - sqrt(15) + 5 =
8 - 2*sqrt(15)

#7
sqrt(x + 5) = 8
Square both sides:
x + 5 = 64
x = 59

Hope this helps.

Jeff