Question

is the number (3+√5) (3-√5) rational or irrational?​

Answer 1

(3+√5) (3-√5)=3^2-(√5)^2=9-5=4.

So,4 is a rational number because it can be expressed as the quotient of two integers: 4 ÷ 1.

Answer 2

$(3 + \sqrt{5})(3 - \sqrt{5} ) \\ using \: identity \: (x + y)(x - y) = {x}^{2} - {y}^{2} \\ = {3}^{2} - {( \sqrt{5)} }^{2} \\ 9 - 5 \\ = 4 \\ \\ therefore \: it \: is \: a \: rational \: number$

there you go :)