Question Number 221245 by fantastic last updated on 28/May/25
$${Which}\:{is}\:{greater}\:\:\:\:\:\:\:\left(\sqrt{\mathrm{7}}+\mathrm{1}\right)\:\:{or}\:\:\left(\sqrt{\mathrm{3}}+\sqrt{\mathrm{5}}\right)????? \\ $$
Answered by mr W last updated on 28/May/25
$$\left(\sqrt{\mathrm{7}}+\mathrm{1}\right)^{\mathrm{2}} =\mathrm{8}+\mathrm{2}\sqrt{\mathrm{7}} \\ $$$$\left(\sqrt{\mathrm{3}}+\sqrt{\mathrm{5}}\right)^{\mathrm{2}} =\mathrm{8}+\mathrm{2}\sqrt{\mathrm{15}}>\mathrm{8}+\mathrm{2}\sqrt{\mathrm{7}}=\left(\sqrt{\mathrm{7}}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\Rightarrow\sqrt{\mathrm{3}}+\sqrt{\mathrm{5}}>\sqrt{\mathrm{7}}+\mathrm{1} \\ $$