Show that is an irrational.

Foundation

Mathematics Foundation

Properties of Real Number

Irrational Number

Algebraic Identities

Question

Show that $(\sqrt{3} + \sqrt{5})^{2}$ is an irrational.

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$(\sqrt{3} + \sqrt{5})^{2} = (\sqrt{3})^{2} + (\sqrt{5})^{2} + 2 \sqrt{3} \sqrt{5}$

= 3 + 5 + 2 \sqrt{15}

= 8 + 2 \sqrt{15}

which is an irrational number