Question Number 180776 by Acem last updated on 17/Nov/22
$${Simplify}\:\:\sqrt{\frac{\mathrm{4}}{\:\sqrt{\mathrm{2}}}\:+\:\mathrm{3}}\: \\ $$$$ \\ $$
Answered by BaliramKumar last updated on 17/Nov/22
$$\sqrt{\frac{\mathrm{4}}{\:\sqrt{\mathrm{2}}}\:+\:\mathrm{3}\:} \\ $$$$\sqrt{\mathrm{2}\sqrt{\mathrm{2}\:}\:+\:\mathrm{3}\:} \\ $$$$\sqrt{\left(\sqrt{\mathrm{2}}\:+\:\mathrm{1}\right)^{\mathrm{2}} \:} \\ $$$$\sqrt{\mathrm{2}}\:+\:\mathrm{1}\:{Answer} \\ $$
Commented by Acem last updated on 17/Nov/22
$${Good}!\:,\:{Thanks} \\ $$
Answered by manxsol last updated on 17/Nov/22
$$ \\ $$$$\sqrt{\frac{\mathrm{4}}{\:\sqrt{\mathrm{2}}}+\mathrm{3}}=\sqrt{{a}}+\sqrt{{b}} \\ $$$$\mathrm{2}\sqrt{\mathrm{2}}+\mathrm{3}={a}+{b}+\mathrm{2}\sqrt{{ab}} \\ $$$${a}+{b}=\mathrm{3} \\ $$$${ab}=\mathrm{2} \\ $$$${t}^{\mathrm{2}} −\mathrm{3}{t}+\mathrm{2}=\mathrm{0} \\ $$$$\left({t}−\mathrm{2}\right)\left({t}−\mathrm{1}\right) \\ $$$${a}=\mathrm{2} \\ $$$${b}=\mathrm{1} \\ $$$$\sqrt{\frac{\mathrm{4}}{\:\sqrt{\mathrm{2}}}+\mathrm{3}}=\:\mathrm{1}+\sqrt{\mathrm{2}} \\ $$
Commented by Acem last updated on 17/Nov/22
$${Good}\:{too}!,\:{Thanks} \\ $$