Question

31. Examine whether(√2+√3)^2 number is rational or irrational.​

Answer 1

Step-by-step explanation:

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State whether (√2+√3)² is rational or irrational

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$\implies {( \sqrt{2} + \sqrt{3} )}^{2} \\ \\ we \: know \: that = > \\ \\ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ \implies { (\sqrt{2} )}^{2} + {( \sqrt{3} )}^{2} + 2( \sqrt{2} \times \sqrt{3} ) \\ \\ \implies 2 + 3 + 2 \sqrt{6} \\ \\ \implies 5 + 2 \sqrt{6} \\ \\ we \: know \: that \: \sqrt{6} \: is \: irrational \\ \\ so \: \: 5 + 2 \sqrt{6} \: is \: irrational$