Maharashtra BoardEnglish MediumSTD 9MathsNumber System1 Mark
Question
Examine, whether the following numbers are rational or irrational:$\big(\sqrt{2}+\sqrt{3}\big)^2$
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Answer
$\big(\sqrt{2}+\sqrt{3}\big)^2$We have,
$\big(\sqrt{2}+\sqrt{3}\big)^2=2+2\sqrt{6}+3=5+\sqrt{6}$$\left[\right.$ Since, $\left.(a+b)^2=a^2+2 a b+b^2\right]$
The sum of a rational number and an irrational number is an irrational number, so $\big(\sqrt{2}+\sqrt{3}\big)^2$ is an irrational number.
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