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Question Number 176839 by Ar Brandon last updated on 27/Sep/22

If a=2+(√(15)) Express (((√(15))+((196)/(54))))^(1/3) in terms of a

$$\mathrm{If}\:{a}=\mathrm{2}+\sqrt{\mathrm{15}}\:\:\mathrm{Express} \\ $$$$\:\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{15}}+\frac{\mathrm{196}}{\mathrm{54}}}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{a} \\ $$

Answered by Rasheed.Sindhi last updated on 27/Sep/22

If a=2+(√(15)) Express (((√(15))+((196)/(54))))^(1/3) in terms of a (((√(15))+((196)/(54))))^(1/3) =(((√(15))+3((17)/(27))))^(1/3) =(((√(15))+2+1((17)/(27))))^(1/3) =((a+1((17)/(27))))^(1/3)

$$\mathrm{If}\:{a}=\mathrm{2}+\sqrt{\mathrm{15}}\:\:\mathrm{Express} \\ $$$$\:\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{15}}+\frac{\mathrm{196}}{\mathrm{54}}}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{a} \\ $$$$\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{15}}+\frac{\mathrm{196}}{\mathrm{54}}}\:=\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{15}}+\mathrm{3}\frac{\mathrm{17}}{\mathrm{27}}}\: \\ $$$$=\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{15}}+\mathrm{2}+\mathrm{1}\frac{\mathrm{17}}{\mathrm{27}}}\:=\sqrt[{\mathrm{3}}]{{a}+\mathrm{1}\frac{\mathrm{17}}{\mathrm{27}}}\: \\ $$

Answered by Frix last updated on 27/Sep/22

((((196)/(54))+(√(15))))^(1/3) =((2+(√(15)))/3)

$$\sqrt[{\mathrm{3}}]{\frac{\mathrm{196}}{\mathrm{54}}+\sqrt{\mathrm{15}}}=\frac{\mathrm{2}+\sqrt{\mathrm{15}}}{\mathrm{3}} \\ $$

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