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Surds & indices in business mathematics

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Surds & indices in business mathematics

1. 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
2. 2. My words..... My purpose here is to give a few questions, which are often asked in aptitude tests and competitive examinations. Please prepare well for your examinations. Please pass this presentation to all those who might need it. Let us spread knowledge as widely as possible. I welcome your suggestions. I also request you to help me in spreading social entrepreneurship across the globe – for which I need support of you people – not of any VIP. With your help, I can spread the ideas – for which we stand....
3. 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. 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. 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. 6. What is the value of 3^7 * 3 ^-5 ? We can put it as : 3 ^ (7 – 5) =3^2 = 9 answer
7. 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. 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. 9. What is the value of (90/250)^1/2 ? Solving this we get : (9/25)^(1/2) =3/5 answer
10. 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. 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. 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. 13. Simplify : We know that 96=4*4*6 we can write it as : 4 *sqrt(6) answer
14. 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. 15. What will you get from : 16^(3/2) ? = 16 ^ (½ *3) 4^3 =64 answer
16. 16. What will you get : 512^(2/9)? =512^(1/9 * 2) =(2^9)^(1/9 * 2) =2^2 =4 answer
17. 17. What do you get from : (1/81)^(-5/4)? =(81)^(5/4) =(3^4)^(5/4) =3^5 =243 answer
18. 18. What will you get from (256/81)^(-3/4) ? =(81/256)^(3/4) =(3/4)^3 =27/64 answer
19. 19. What will you get from : (.0000012/.00003)^(-1/2)? =(.04)^(-1/2) =(1/.04)^(1/2) =1/.2 =5 answer
20. 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. 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. 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. 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. 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. 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