Theory of indices Problems:

1. A certain number of persons agree to subscribe as many rupees each as there are subscribers. The whole subscription is Rs.2582449. Find the number of subscriber?

Let the number of subscribers be x, say since each subscriber agrees to
subscribe x rupees.
The total subscription = no. of persons × subscription per person
= x × x = x2
X2=2582449
∴x = 1607


2. Simplify: 3√192a3b4
Use the 2 formulas
(abc)m=ambmcm
(am)n=amn
3√192a3b4=(192a3b4)1/3
                =(192)1/3.(a3)1/3(b4)1/3
                =(26 x3).ab4/3
                =22.31/3.ab4/3
                =4a.(3b4)1/3
                =4a.3√3b4

3.simplify 3√x9y12
          Solution:3√x9y12=(x9y12)1/3
                                             =(x9)1/3(y12)1/3
                                                   =x3y4


  4.Find the number whose square is equal to the difference between the squares of
75.12 and 60.12
Let ‘x’ be the number required
∴x2 = (75.12)2 – (60.12)2
= (75.12 + 60.12) (75.12 – 60.12)
= 135.24 ×15 = 2028.60

∴x2 = √2028.60 = 45.0399


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