The smallest among, \sqrt ^6 {12},\sqrt^ 3 {4}, \sqrt^4 {5}, \sqrt{3} is

SSC CPO SI and ASI 2011 Paper

Question : 105 of 200

Marks: +1, -0

The smallest among,

√ ^6 {12},√^ 3 {4}, √^4 {5}, √{3}

Solution:

(4) LCM of indices surds = LCM of 6, 3, 4 and 2 = 12.
So

√^6 12=√^12 12^2=√^12 144

√^3 4 =√^12 4^4=√^12 256

√^4 5 = √^12 5^3=√^12 125

and

√3 =√^12 3^6 = √^12 729

Therefore, the smallest surd is

√^12 125 = √^4 5

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