Question

State True or False:

$(\sqrt{2}+\sqrt{3}{)}^2$ is an irrational number.

• A. True
• B. False

Answer 1

The correct option is A True

${(\sqrt{2}+\sqrt{3})}^2=2+3+2\sqrt{6}=5+2\sqrt{6}\sqrt{6}=\mathrm{2.44948974278........}$

Here,$\sqrt{6}$ is an irrational number, since its decimal representation is non-terminating repeating.

Hence, ${(\sqrt{2}+\sqrt{3})}^2$ is an irrational number.

therefore, the statement is true.