Maharashtra BoardEnglish MediumSTD 9MathsNumber System1 Mark
Question
Examine, whether the following numbers are rational or irrational:$\big(2-\sqrt{2}\big)\big(2+\sqrt{2}\big)$
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Answer
$\big(2-\sqrt{2}\big)\big(2+\sqrt{2}\big)$We have,
$(2-\sqrt{2})(2+\sqrt{2})=(2)^2-(\sqrt{2})^2\left[\right.$ Since, $\left.(a+b)(a-b)=a^2-b^2\right]$
$4-2=\frac{2}{1}$
Since, 2 is a rational number.
$\big(2-\sqrt{2}\big)\big(2+\sqrt{2}\big)$ is a rational number.
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