Quantitative Aptitude Ques 2354

Question: If $ x=\sqrt{a\sqrt[3]{b\sqrt{a\sqrt[3]{b…..\infty }}}}, $ then the value of x is

Options:

A) $ \sqrt[5]{ab^{3}} $

B) $ \sqrt[5]{a^{5}b} $

C) $ \sqrt[3]{a^{3}b} $

D) $ \sqrt[5]{a^{3}b} $

Show Answer

Answer:

Correct Answer: D

Solution:

  • Given, $ x=\sqrt{a\sqrt[3]{b\sqrt{a\sqrt[3]{b…..\infty }}}} $ By squaring both sides, $ x^{2}=a\sqrt[3]{b\sqrt{a\sqrt[3]{b…..\infty }}} $ By cubing both sides, $ x^{6}=a^{3}b\sqrt{a\sqrt[3]{b…..\infty }} $

$ \Rightarrow $ $ x^{6}=a^{3}bx $

$ \Rightarrow $ $ x^{6}-a^{3}bx=0 $

$ \Rightarrow $ $ x,(x^{5}-a^{3}b)=0 $

$ \Rightarrow $ $ x=0, $ $ x^{5}=a^{3}b $

$ \therefore $ $ x=\sqrt[5]{a^{3}b} $

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