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Question Number 148042 by mathdanisur last updated on 25/Jul/21

(√(17 − 4(√(15)))) − ((144))^(1/4)  = ?

$$\sqrt{\mathrm{17}\:−\:\mathrm{4}\sqrt{\mathrm{15}}}\:−\:\sqrt[{\mathrm{4}}]{\mathrm{144}}\:=\:? \\ $$

Answered by Olaf_Thorendsen last updated on 25/Jul/21

X = (√(17−4(√(15))))−((144))^(1/4)   X = (√((2(√3)−(√5))^2 ))−((12^2 ))^(1/4)   X = 2(√3)−(√5)−(√(12))  X = 2(√3)−(√5)−2(√3)  X = −(√5)

$$\mathrm{X}\:=\:\sqrt{\mathrm{17}−\mathrm{4}\sqrt{\mathrm{15}}}−\sqrt[{\mathrm{4}}]{\mathrm{144}} \\ $$$$\mathrm{X}\:=\:\sqrt{\left(\mathrm{2}\sqrt{\mathrm{3}}−\sqrt{\mathrm{5}}\right)^{\mathrm{2}} }−\sqrt[{\mathrm{4}}]{\mathrm{12}^{\mathrm{2}} } \\ $$$$\mathrm{X}\:=\:\mathrm{2}\sqrt{\mathrm{3}}−\sqrt{\mathrm{5}}−\sqrt{\mathrm{12}} \\ $$$$\mathrm{X}\:=\:\mathrm{2}\sqrt{\mathrm{3}}−\sqrt{\mathrm{5}}−\mathrm{2}\sqrt{\mathrm{3}} \\ $$$$\mathrm{X}\:=\:−\sqrt{\mathrm{5}} \\ $$

Commented by mathdanisur last updated on 25/Jul/21

Thank you Ser

$${Thank}\:{you}\:{Ser} \\ $$

Commented by tabata last updated on 25/Jul/21

msr olaf can you help me in question 148064 please sir

$${msr}\:{olaf}\:{can}\:{you}\:{help}\:{me}\:{in}\:{question}\:\mathrm{148064}\:{please}\:{sir} \\ $$$$ \\ $$

Answered by liberty last updated on 25/Jul/21

(√(17−2(√(60)) )) =(√((12+5)−2(√(12×5))))  = (√(12))−(√5)  ∴ (√(27−4(√(15)))) −((144))^(1/4)  = (√(12))−(√5)−(√(12)) =−(√5)

$$\sqrt{\mathrm{17}−\mathrm{2}\sqrt{\mathrm{60}}\:}\:=\sqrt{\left(\mathrm{12}+\mathrm{5}\right)−\mathrm{2}\sqrt{\mathrm{12}×\mathrm{5}}} \\ $$$$=\:\sqrt{\mathrm{12}}−\sqrt{\mathrm{5}} \\ $$$$\therefore\:\sqrt{\mathrm{27}−\mathrm{4}\sqrt{\mathrm{15}}}\:−\sqrt[{\mathrm{4}}]{\mathrm{144}}\:=\:\sqrt{\mathrm{12}}−\sqrt{\mathrm{5}}−\sqrt{\mathrm{12}}\:=−\sqrt{\mathrm{5}} \\ $$

Commented by mathdanisur last updated on 25/Jul/21

Thanks Sir

$${Thanks}\:{Sir} \\ $$

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