How to add, subtract, mutiply, and divide square roots?

Question

f(x)= √(3-x) and g(x)= √(x^2 - 1)

what is:
a) f+g
b) f-g
c) fg
d) f/g

Answer 1

(a)

f(x)= √(3-x) and g(x)= √(x^2 - 1)

f+g = (√(3-x)) + (√(x^2 - 1))

If the radical is the same in each term (namely, the square root of expression), we can combine the terms.

But here in this case two different radicals are given so we can't simplify it further

(b)

f-g =  (√(3-x)) - (√(x^2 - 1))

(c)

fg =  (√(3-x)) × (√(x^2 - 1))

(d)

f/g =  (√(3-x)) / (√(x^2 - 1))