Question Number 82082 by TawaTawa last updated on 18/Feb/20
$$\mathrm{Evaluate}:\:\:\:\:\:\:\left(\frac{\sqrt{\mathrm{30}\:+\:\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}}{\:\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}\right)^{\mathrm{1}/\mathrm{4}} \\ $$
Commented by MJS last updated on 18/Feb/20
$$\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{expand}\:\mathrm{or}\:\mathrm{factorise}\:\sqrt{\mathrm{30}+\sqrt{\mathrm{8}}+\sqrt{\mathrm{5}}}\: \\ $$$$\Rightarrow\:\mathrm{we}\:\mathrm{can}\:\mathrm{only}\:\mathrm{use}\:\mathrm{a}\:\mathrm{calculator} \\ $$
Commented by jagoll last updated on 18/Feb/20
$${let}\:\sqrt{\mathrm{8}}+\sqrt{\mathrm{5}}\:=\:{t} \\ $$$$\sqrt[{\mathrm{4}\:}]{\frac{\sqrt{\mathrm{30}+{t}}}{{t}}\:}\:=\:\sqrt[{\mathrm{4}\:}]{\frac{\sqrt{\mathrm{30}+{t}}}{\:\sqrt{{t}^{\mathrm{2}} }}}\:=\:\sqrt[{\mathrm{4}\:}]{\frac{\mathrm{30}+{t}}{\:\sqrt{{t}^{\mathrm{3}} +\mathrm{30}{t}^{\mathrm{2}} }}} \\ $$
Commented by jagoll last updated on 18/Feb/20
$${haha}..{i}\:{don}'{t}\:{have}\:{idea} \\ $$
Commented by john santu last updated on 18/Feb/20
$${haha}…. \\ $$