How To Simplify Radicals

How To Simplify Radicals A radical of a positive real quantity is called a surd if its value cannot exactly determine. Radical is represented by root , whether it can be square root or cube root. Thus, each of the quantities 3, (16) ^ (2/3), (7) ^ (1/5) etc., a radical. From the definition it is evident that a radical is an incommensurable quantity, although its value can be determined to any degree of accuracy should not be noted that quantities 4, (27) ^ (1/3), (16 / 81) ^ (1/4) etc., expressed in the form radical are commensurable quantities are not radical because 4 = 2 (27) ^ (1/3) = 3 (16 / 81) ^ (1/4) = 2 / 3 In fact, any root of an algebraic expression regarded as a radical. Question 1: - 32 2 18 + 5 2 + 2 ^ (3/2) Solution: - 32 2 18 + 5 2 + 2 ^ (3/2)= (16 * 2) 2 (9*2) + 5 2 +(2^3) =42 - 62 +52+22 =(4-6+5+2) 2 =52 Answer: - 52 Question 2: - Simplify: 32 x 5 (4)^(1/3) x 4 (8)^(1/4) Solution: - 32 x 5 (4) ^(1/3) x 4 (8)^(1/4) = (3x5x4)x[2^(1/2) x 4^(1/3) x 8^(1/4)] = 60 x 2^ (1/2) x 2^(2/3) x 2^(3/4) = 60 x 2^ (1/2 + 2/3 + ) = 60 x 2^ (23/12) = 60 x (2^23) ^(1/12) =60 x [2^ (12+11)] ^(1/12) = 60 x (2^12 x 2^11)^(1/12) = 60 x 2 x(2^11)^(1/12) = 120 x (2048)^ (1/2) = 120 (2048)^(1/2)