Question

show that (√3+√5)² is an irrational​

Answer 1

$\textit{\large{\pink{\underline{\underline{Step by step Explanation:-}}}}}$

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

$\mathrm{=3+2\sqrt{15}+5}$

$\mathrm{=3+2\sqrt{15}+5}$

$\mathrm{=8+2\sqrt{15}}$

Because,,$\mathrm{</strong><strong>[</strong><strong>\sqrt{15}</strong><strong>]</strong><strong>}$ is an irrational number.So,,$\mathrm{</strong><strong>[</strong><strong>(8+2\sqrt{15}</strong><strong>)</strong><strong>]</strong><strong>}$ is also an irrational number..Hence$\mathrm{</strong><strong>[</strong><strong>(\sqrt{3}+\sqrt{5})^2</strong><strong>]</strong><strong>}$ is an irrational number..

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