This document provides a summary of concepts related to surds and indices in business mathematics. It includes example problems and solutions involving operations with surds, indices, and fractions with surds and indices. The document was created by Dr. T.K. Jain for students of CSE and PGPSE programs. It encourages students to prepare well for exams and provides links to download additional educational resources.

1. SURDS & INDICES IN BUSINESS MATHEMATICS by : DR. T.K. JAIN AFTERSCHO ☺ OL centre for social entrepreneurship sivakamu veterinary hospital road bikaner 334001 rajasthan, india FOR – CSE & PGPSE STUDENTS (CSE & PGPSE are free online programmes open for all, free for all) mobile : 91+9414430763

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3. What is the value of (81X^4Y^8)^(1/4) 81 can be written as : 3^4 thus we can write it as : (all the powers gets cancelled) (3Xy^2) answer

4. What is the value of (256/81)^(1/4)? 256=4^4 = (4/3) ^ 4 * ¼ so answer is : 4/3 (as all the powers get cancelled). Answer

5. What is the value of (1/1024)^(-1/10)? In order to remove negative sign, we put it like this : = (1024)^(1/10) we know that 1024 = 2^10 = (1/2)^10 *1/10 = ½ answer

6. What is the value of 3^7 * 3 ^-5 ? We can put it as : 3 ^ (7 – 5) =3^2 = 9 answer

7. Find the value of 2^(-1/10) * 1024^(1/4)? Options : 2, 4, 16, none of these answer : none of these =(1/2)^(1/10) * 1024^(1/4) =1/2^(1/10)*512^(1/2) answer

8. What is the value of (75/243)^(-1/2)? In order to remove negative sign, first reverse these : (243 / 75) ^ (½) both the numbers are divisible by 3, so : (81/25)^1/2 we can write it as : (81)^1/2 / (25)^1/2 =9/5 answer

9. What is the value of (90/250)^1/2 ? Solving this we get : (9/25)^(1/2) =3/5 answer

10. What is the value of : Let us multiply 4*3 and let us multiply sqrt(3) we get : 4*3*3 = 36 answer

11. What is the value of 28 = 4*7 sqrt of 4 = 2, so 2 can be multiplied to 3. It can be written as : 5 – 6 (sqrt (7)) =-sqrt(7) answer

12. What is the value of : In order to simplify it, multiply it by : the value of its denominator we get : (2*3*sqrt(5)) / (9*5) =6*sqrt(5)/45 =2(sqrt(5))/15 answer

13. Simplify : We know that 96=4*4*6 we can write it as : 4 *sqrt(6) answer

14. Simplify : In order to simplify, we have to multiply it with 2+(sqrt(2)) we get : 3(2+sqrt(2)) / (4-2) =6 + (sqrt(2)) / 2 =3 + 1/(sqrt(2)) answer

15. What will you get from : 16^(3/2) ? = 16 ^ (½ *3) 4^3 =64 answer

16. What will you get : 512^(2/9)? =512^(1/9 * 2) =(2^9)^(1/9 * 2) =2^2 =4 answer

17. What do you get from : (1/81)^(-5/4)? =(81)^(5/4) =(3^4)^(5/4) =3^5 =243 answer

18. What will you get from (256/81)^(-3/4) ? =(81/256)^(3/4) =(3/4)^3 =27/64 answer

19. What will you get from : (.0000012/.00003)^(-1/2)? =(.04)^(-1/2) =(1/.04)^(1/2) =1/.2 =5 answer

20. RULE : a^0 = 1 IF ZERO IS PUT AS POWER OF ANY NUMBER, IT WILL BECOME 1. THUS IF YOU PUT POWER OF ZERO ON 100000, IT WILL BE EQUAL TO 1.

21. RULE : (a/b)^n = a^n / b^n IF YOU TAKE UP POWER OVER A FRACTION, YOU CAN PUT IT SEPARATELY ALSO. EXAMPLE : (2/3) ^3 = 8/27 ANSWER

22. (27)^2/3 =? 1. FIRST WE PUT 27 AS 3^3 BECAUSE WE KNOW 3*3*3 = 27 = (3^3)2/3 WE CAN CANCEL POWR OF 3 3^2 = 9. ANSWER

23. (1024)^-4/5 =? 1. FIRST PUT 1024 AS 2^X, WE KNOW THAT 2*2*2*2*2..... (TILL 10) = 1024 SO WE CAN WRITE : 1024 = 2^10 = 4^5 (4^5)-4/5 (NOW CANCEL 5) = (4)-4= 1/(4)4 (ANY POWER IN NEGATIVE WILL PUT THE NUMERATOR INTO DENOMINATOR) = 1/256.

24. If 2^(x-1)+ 2^(x+1) = 256 then find the value of x .(X-1) * (X+1) = (X^2 – 1) So we can write it as : =2^(x^2-1) = 256 now factorise 256 = 2*2*2*2*2*2*2*2=2^8 2^(x^2 -1) = 2^8 or X^2 = 9 X = 3 answer

25. Simplify : 125^(2/3) * 25^(1/2)*5*5^(1/2) 125^(2/3) = (5^3)^(2/3) 3 gets cancelled so : 5^2 = 25 =5*5 we can write it as : 5*5*5*5*5^(1/2) =5^4 * 5^ (½) (add the two powers, when there is multiplication of their base) =5^(9/2) answer

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