Aptitude Day 217

Problems on Surds and Indices:

1. Find the value of (2^1/4-1)(2^3/4+2^1/2+2^1/4+1)

Solution:

                  Let us assume 2^1/4 = x

  

                  Then  (2^1/4-1)(2^3/4+2^1/2+2^1/4+1) becomes  (x-1)(x³+x²+x+1)

                   (x-1)(x³+x²+x+1)= (x-1)[x²(x+1)+x+1]

                                                 =(x-1)(x+1)(x²+1)

                                                 = (x⁴-1)

                                                 = 2^1(4)/4-1 = 2-1

                                                 = 1.

2. The value of 1/(216)^-2/3  +   1/(256)^-3/4   +   1/(32)^-1/5 is :

      

  Solution:

                 1/(216)^-2/3  +   1/(256)^-3/4   +   1/(32)^-1/5

                 1/(6³)^-2/3  +   1/(4⁴)^-3/4   +   1/(2⁵)^-1/5

                 6²+ 4³+ 2 = 36+ 64+ 2
                                  =102.