x=aabaab−−√3−−−−−√−−−−−−−−√3−−−−−−−−−−−√....∝x=aabaab33....∝x = \sqrt {a\root 3 \of {ab\sqrt {a\root 3 \of {ab} } } } .... \propto then the value of x is?" /> x=aabaab−−√3−−−−−√−−−−−−−−√3−−−−−−−−−−−√....∝x=aabaab33....∝x = \sqrt {a\root 3 \of {ab\sqrt {a\root 3 \of {ab} } } } .... \propto then the value of x is?" /> x=aabaab−−√3−−−−−√−−−−−−−−√3−−−−−−−−−−−√....∝x=aabaab33....∝x = \sqrt {a\root 3 \of {ab\sqrt {a\root 3 \of {ab} } } } .... \propto then the value of x is?" />

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If $x = \sqrt{a \sqrt[3]{a b \sqrt{a \sqrt[3]{a b}}}} . . . . \propto$ $x = \sqrt {a\root 3 \of {ab\sqrt {a\root 3 \of {ab} } } } .... \propto$ then the value of x is?

1 $\sqrt[5]{a^{2} b}$ $\root 5 \of {{a^2}b}$
2 $\sqrt[5]{a^{4} b^{4}}$ $\root 5 \of {{a^4}{b^4}}$
3 $\sqrt[6]{a^{5} b}$ $\root 6 \of {{a^5}b}$
4 $\sqrt[5]{a^{4} b}$ $\root 5 \of {{a^4}b}$

Answer:- 1

Explanation:-

Solution:

\begin{aligned} x = \sqrt{a \sqrt[3]{a b \sqrt{a \sqrt[3]{a b}}}} . . . . . . . \propto \\ Square both sides \\ x^{2} = a \sqrt[3]{a b x} (∴ \sqrt{a \sqrt[3]{a b}} . . . . \propto) \\ Again cube both sides \\ x^{6} = a^{3} a b x \\ x^{5} = a^{4} b \\ x = \sqrt[5]{a^{4} b} \end{aligned}

$\eqalign{ & x = \sqrt {a\root 3 \of {ab\sqrt {a\root 3 \of {ab} } } } ....... \propto \cr & {\text{Square both sides}} \cr & {x^2} = a\root 3 \of {abx} {\text{ }}\left( {\therefore \sqrt {a\root 3 \of {ab} } .... \propto } \right) \cr & {\text{Again cube both sides}} \cr & {x^6} = {a^3}abx \cr & {x^5} = {a^4}b \cr & x = \root 5 \of {{a^4}b} \cr}$

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then the value of x is?", "text": "If

x = \sqrt{a \sqrt[3]{a b \sqrt{a \sqrt[3]{a b}}}} . . . . \propto

$x = \sqrt {a\root 3 \of {ab\sqrt {a\root 3 \of {ab} } } } .... \propto$ then the value of x is?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} x = \sqrt{a \sqrt[3]{a b \sqrt{a \sqrt[3]{a b}}}} . . . . . . . \propto \\ Square both sides \\ x^{2} = a \sqrt[3]{a b x} (∴ \sqrt{a \sqrt[3]{a b}} . . . . \propto) \\ Again cube both sides \\ x^{6} = a^{3} a b x \\ x^{5} = a^{4} b \\ x = \sqrt[5]{a^{4} b} \end{aligned}

$\eqalign{ & x = \sqrt {a\root 3 \of {ab\sqrt {a\root 3 \of {ab} } } } ....... \propto \cr & {\text{Square both sides}} \cr & {x^2} = a\root 3 \of {abx} {\text{ }}\left( {\therefore \sqrt {a\root 3 \of {ab} } .... \propto } \right) \cr & {\text{Again cube both sides}} \cr & {x^6} = {a^3}abx \cr & {x^5} = {a^4}b \cr & x = \root 5 \of {{a^4}b} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} x = \sqrt{a \sqrt[3]{a b \sqrt{a \sqrt[3]{a b}}}} . . . . . . . \propto \\ Square both sides \\ x^{2} = a \sqrt[3]{a b x} (∴ \sqrt{a \sqrt[3]{a b}} . . . . \propto) \\ Again cube both sides \\ x^{6} = a^{3} a b x \\ x^{5} = a^{4} b \\ x = \sqrt[5]{a^{4} b} \end{aligned}

$\eqalign{ & x = \sqrt {a\root 3 \of {ab\sqrt {a\root 3 \of {ab} } } } ....... \propto \cr & {\text{Square both sides}} \cr & {x^2} = a\root 3 \of {abx} {\text{ }}\left( {\therefore \sqrt {a\root 3 \of {ab} } .... \propto } \right) \cr & {\text{Again cube both sides}} \cr & {x^6} = {a^3}abx \cr & {x^5} = {a^4}b \cr & x = \root 5 \of {{a^4}b} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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