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Question Number 82082 by TawaTawa last updated on 18/Feb/20

Evaluate:      (((√(30 + (√8) + (√5)))/((√8) + (√5))))^(1/4)

$$\mathrm{Evaluate}:\:\:\:\:\:\:\left(\frac{\sqrt{\mathrm{30}\:+\:\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}}{\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}\right)^{\mathrm{1}/\mathrm{4}} \\ $$

Commented by MJS last updated on 18/Feb/20

it′s not possible to expand or factorise (√(30+(√8)+(√5)))   ⇒ we can only use a calculator

$$\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{expand}\:\mathrm{or}\:\mathrm{factorise}\:\sqrt{\mathrm{30}+\sqrt{\mathrm{8}}+\sqrt{\mathrm{5}}}\: \\ $$$$\Rightarrow\:\mathrm{we}\:\mathrm{can}\:\mathrm{only}\:\mathrm{use}\:\mathrm{a}\:\mathrm{calculator} \\ $$

Commented by jagoll last updated on 18/Feb/20

let (√8)+(√5) = t  ((((√(30+t))/t) ))^(1/(4 ))  = (((√(30+t))/(√t^2 )))^(1/(4 ))  = (((30+t)/(√(t^3 +30t^2 ))))^(1/(4 ))

$${let}\:\sqrt{\mathrm{8}}+\sqrt{\mathrm{5}}\:=\:{t} \\ $$$$\sqrt[{\mathrm{4}\:}]{\frac{\sqrt{\mathrm{30}+{t}}}{{t}}\:}\:=\:\sqrt[{\mathrm{4}\:}]{\frac{\sqrt{\mathrm{30}+{t}}}{\sqrt{{t}^{\mathrm{2}} }}}\:=\:\sqrt[{\mathrm{4}\:}]{\frac{\mathrm{30}+{t}}{\sqrt{{t}^{\mathrm{3}} +\mathrm{30}{t}^{\mathrm{2}} }}} \\ $$

Commented by jagoll last updated on 18/Feb/20

haha..i don′t have idea

$${haha}..{i}\:{don}'{t}\:{have}\:{idea} \\ $$

Commented by john santu last updated on 18/Feb/20

haha....

$${haha}.... \\ $$

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