Question 1044936

How do I give an example of a binomial in the form a√b+c√d and its conjugate. Then find their product?
<pre>{{{a * sqrt(b) + c * sqrt(d)}}}
With a  = 1; b= 3, c = 5, d = 7, we get: {{{matrix(1,3, 1 * sqrt(3) + 5 * sqrt(7), "=", sqrt(3) + 5sqrt(7))}}}
Its conjugate: {{{sqrt(3) - 5sqrt(7)}}}
Product: {{{highlight_green((sqrt(3) + 5sqrt(7))(sqrt(3) - 5sqrt(7)) = 3 - 5sqrt(21) + 5sqrt(21) - 25 (7) = 3 - 175 = highlight(- 172)))}}}