" 6.(i) "root(4)(15)

Compare : (i) root(6 )(15) and root(4)(12)" (ii) "sqrt(24) and root(3)(25)

Using differentials, find the approximate values of the following: (i) root(4)15 (ii)(82)^(1//4)

The following are the steps involved in finding the least amont sqrt(3),root(3)(4) and root(6)(15) . Arrange them in sequential order. (A) therefore root(6)(15) is the smallest (B) therefore 3^(1//2)=3^(3//6), 4^(1//3)=4^(2//6), 15^(1//6)=15^(1//6) (C)The LCM fo the denominators of the exponents is 6 (D) sqrt(3)=3^(1//2), root(3)(4)=4^(1//3), root(6)(15)=15^(1//6) (E) therefore sqrt(3)=root(6)(27), root(3)(4)=root(6)(16)root(6)(15)=root(6)(15)

The greatest among the numbers root(4)(2),root(5)(3),root(10)(6) and root(20) (15) is

(i) Simplify (2^(2/3)-2^((-2)/3))(2^(4/3)+1+2^((-4)/3)) (ii) [(root(6)(7))^(2)+(root(6)(7))^(-2)][(root(6)(7))^(4)-1+(root(6)(7))^(-4)]

(a) sqrt15xxsqrt35. (b) 2sqrt3 div3sqrt27. (c ) Muliple root(3)(3)" by " root(4)(2). (d) Divide ""root(6)(5)" by "root(3)(10).

root(3)(4) times root(6)(5)