CMAT 2017 Solved Question Paper

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Question : 24 of 100

Marks: +1, -0

If

x = √{a \; √^3{b√{a \;\ √^3{b} ........∞}}}

, then the value of x is :

$^5{√ {a^3b }}$
$^3{√ {a^5b }}$
$^3{√ {ab^3 }}$
$^3{√ {a^3b }}$

Solution:

Given

x = √{a \; √^3{b√{a \;\ √^3{b} .............∞}}}

On squaring both sides, we get

x^{2}=a \html ' ' {\;√^3{b√{a \;\;^3√{b...∞}}}}

Now taking cube of both sides, we get⇒

x^5=a^3bx

⇒

x^5= a^3b

Now taking

1/5

th root of x we get
⇒

x= √^5{a^3b}

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