Question 718131
a) 3 is rational
b) Multiply the numerator and denominator by {{{sqrt(p)+sqrt(p^2-1)}}}. This will be easier if you think of {{{sqrt(p)}}} as "a" and {{{sqrt(p^2-1)}}} as "b" and use the {{{(a+b)^2 = a^2+2ab+b^2}}} pattern to multiply the numerators and the {{{(a-b)(a+b) = a^2-b^2}}} pattern to multiply the denominators. (The second pattern, in fact, is how you figure out that multiplying by {{{sqrt(p)+sqrt(p^2-1)}}} will help. We already have a ("a"-"b"). If we multiply by the corresponding ("a"+"b") we will get and expression of only perfect squares, making the square roots disappear!)