The greatest among the following numbers (3)^{ \frac{1}{3}},(2)^{ \frac{1}{2}}, 1,(6)^{ \frac{1}{6}} is

SSC CPO SI and ASI 2013 Paper

Question : 135 of 200

Marks: +1, -0

The greatest among the following numbers

(3)^{ {1}/{3}},(2)^{ {1}/{2}}, 1,(6)^{ {1}/{6}}

Solution:

(4) Since, LCM of 3, 2 and 6 = 6

⇒(3)^{ {1}/{3}}=\ (3^{2} )^{ {1}/{6}}=(9)^{ {1}/{6}}

⇒(2)^{ {1}/{2}}= (2^{3} )^{ {1}/{6}}=(8)^{ {1}/{6}}

⇒(1)^{ {1}/{6}}=1

⇒(6)^{ {1}/{6}}

So, the greatest number

=(9)^{ {1}/{6}}=(3)^{ {1}/{3}}

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