Question

Give examples of two irrational numbers whose product is
a - rational numbers and
b - irrational number

Answer 1

➡HERE IS YOUR ANSWER⬇

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Let me tell you something : the product of two conjugated irrational numbers is always a rational number.

Examples :

$1. )\: ( \sqrt{2 } + 1)( \sqrt{2} - 1) = 2 - 1 = 1 \\ \\ 2.) \: ( \sqrt{3} + \sqrt{2} )( \sqrt{3} - \sqrt{2} ) = 3 - 2 = 1$
Also,

$3. )\: \sqrt{2} . \sqrt{2} = 2$

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Again, the product of non-conjugated numbers are always irrational other than standard irrational numbers.

$1.) \: ( \sqrt{5} + 1)( \sqrt{5} - \sqrt{7} ) \\ 2.) \: (\sqrt{17} - \sqrt{3} )( \sqrt{13} - \sqrt{3} ) \\ 3.) \: \sqrt{2}. \sqrt{3} = \sqrt{6}$

⬆HOPE THIS HELPS YOU⬅