Express (7+ √5)/(3+√5) in the form a + b √5, where a and b are integers.

(7+ √5)/(3+√5)Here, the denominator is not rational - (numbers like 2 and 3 are rational). A number with an irrational denominator isn't incorrect, it just isn't in the simplest form it can be in.To rationalise the denominator in this case, we want to use the denominator's conjugate (e.g. Conjugate of 2-√3, would be 2+√3)We do this because it helps remove the surd from the denominator.(7+ √5)/(3+√5) * (3-√5) /(3-√5) (Note that the second part - (3-√5) /(3-√5) - we use this because anything divided by itself equals 1. Multiplying anything by 1 doesn't change it's value)Multiplying fractions (toptop and bottombottom): (7+ √5)(3-√5)/(3+√5)(3-√5) Use FOIL to multiply out brackets and simplify---> 4-√5So, a=4 and b=-1