Examine whether the following number are rational or irrational: … - Vidyadip

Question

Examine whether the following number are rational or irrational:$\big(\sqrt{3}+2\big)^2$

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Answer

$\big(\sqrt{3}+2\big)^2$$=\big(\sqrt{3}\big)^2+2\times2\times\sqrt{3}+(2)^2$
$=3+4\sqrt{3}+4$
$=7+4\sqrt{3}$
Clearly, the given number is irrational.

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