Question

Have three problems and I'm really confused how to solve/simplify
1. 4/3+square root of 5

2. -4/-4+4square root of 2

3. 1/1+ square root of 2

Answer 1

recall that (a-b)(a+b) = a^2-b^2
so, (3+√5)(3-√5) = 9-5 = 4

So, to simplify such fractions, look for the "square conjugate" if you will, of the denominator.

4/(3+√5) = 4(3-√5) / (3+√5)(3-√5)
= 4(3-√5)/4 = 3-√5

And do the others the same way. You can check your answers at wolframalpha.com

For the first one, just enter

4/(3+√5)

in the box and it will show various data about the expression

http://www.wolframalpha.com/input/?i=4%2F%283%2B%E2%88%9A5%29