`(root(6)(5))(root(3)(2))(sqrt(3))(root(12)(6))`=

root(6)((root(2)(5^4))^6)

The following are the steps involved in finding the greatest among root(3)(2),root(6)(3) and sqrt(6) . Arrange them in sequential order. (A) The LCM of the denominators of the exponents is 6. (B) therefore root(6)(216) i.e., sqrt(6) is greatest. (C) root(3)(2)=2^(1//3), root(6)(3)=3^(1//6), sqrt(6)=6^(1//2) (D) 2^(1//3)=2^(2//6), 3^(1//6), 6^(1//2)=6^(3//6) (E) root(3)(2)=root(6)(4)root(6)(3)-root(6)(3),sqrt(6)=root(6)(216)

(root3(3)+root3(2))(root3(9)+root3(4)-root3(6))=

(sqrt(2root(3)(3))*root(3)(3sqrt(2)))/(3sqrt(2sqrt(3))*sqrt(3root(3)(2)))

(root(6)(15-2sqrt(56)))*(root(3)(sqrt(7)+2sqrt(2))) =_______.

sqrt(root(x)(2^(x))root(x^(2))(3^(x^(3)))root(x^(2))(6^(x^(6)))root(x^(4))(9^(x^(10)))) =

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)