Question Number 208502 by Kalebwizeman last updated on 17/Jun/24
Answered by A5T last updated on 17/Jun/24
$$=\sqrt{\mathrm{16}}+\sqrt{\mathrm{15}}−\sqrt{\mathrm{15}}−\sqrt{\mathrm{14}}+...−\sqrt{\mathrm{9}}−\sqrt{\mathrm{8}}=\mathrm{4}−\mathrm{2}\sqrt{\mathrm{2}} \\ $$
Commented by Kalebwizeman last updated on 17/Jun/24
$${kindly}\:{show}\:{more}\:{working}\:{to}\:{make}\:{it}\:{clearer}.\:{Thank}\:{you} \\ $$
Commented by A5T last updated on 17/Jun/24
$${Rationalize}\:\frac{\mathrm{1}}{\:\sqrt{{a}+\mathrm{1}}−\sqrt{{a}}}=\frac{\left(\sqrt{{a}+\mathrm{1}}+\sqrt{{a}}\right)}{\left(\sqrt{{a}+\mathrm{1}}−\sqrt{{a}}\right)\left(\sqrt{{a}+\mathrm{1}}+\sqrt{{a}}\right)} \\ $$$$=\frac{\sqrt{{a}+\mathrm{1}}+\sqrt{{a}}}{\left(\sqrt{{a}+\mathrm{1}}\right)^{\mathrm{2}} −\left(\sqrt{{a}}\right)^{\mathrm{2}} }=\frac{\sqrt{{a}+\mathrm{1}}+\sqrt{{a}}}{{a}+\mathrm{1}−{a}}=\sqrt{{a}+\mathrm{1}}+\sqrt{{a}} \\ $$