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Find whether each of the following is an irrational number or a rational number.
(i) $(\sqrt{5}-3)^2$
(ii) $(5+\sqrt{3})(5-\sqrt{3})$
(i) $(\sqrt{5}-3)^2$
(ii) $(5+\sqrt{3})(5-\sqrt{3})$
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Sol. (i) $(\sqrt{5}-3)^2 = 8-2\sqrt{15}$
So, $(\sqrt{5}-3)^2$ is an irrational number.
(ii) $(5+\sqrt{3})(5-\sqrt{3}) = 25 - 3 = 22$
So, $(5+\sqrt{3})(5-\sqrt{3})$ is a rational number.
So, $(\sqrt{5}-3)^2$ is an irrational number.
(ii) $(5+\sqrt{3})(5-\sqrt{3}) = 25 - 3 = 22$
So, $(5+\sqrt{3})(5-\sqrt{3})$ is a rational number.