Question

give pair of irrational no. whose product is a rational no. (don't want squares eg.root2 * root2)

Answer 1

$(3 + \sqrt{2} )(3 - \sqrt{2} ) \\ = 9 - 4 \\ = 5 \\ \\( 6 + \sqrt{5} )(6 - \sqrt{5} ) \\ = 36 - 5 \\ = 31$

Answer 2

1.)
$(1 - \sqrt{2} )(1 + \sqrt{2} )$

2.)
$(2 - \sqrt{5} )(2 + \sqrt{5} )$

3.)

$( \sqrt{2} - 1)( \sqrt{2} + 1)$

4.)

$( \sqrt{3} - \sqrt{2} )( \sqrt{3} + \sqrt{2)}$