## FeedBack Form

Your Name : : : :
FeedBack

## SURDS AND INDICES -> IMPORTANT FACTS AND FORMULAE

1. LAWS OF INDICES : (i) am * an = am + n (ii)  am / an = am - n (iii)  (am)n = amn (iv)  (ab)n = anbn (v)  (a/b)n = an/ bn (vi)  a0 = 1 SURDS : Let a be rational number and n be a positive integer such that a(1/n) = n√a LAWS OF SURDS : (i)  n√a = a (1/n) (ii)  n√ab = n√a x n√b (iii)  n√a/b = n√a / n√b (iv)  (n√a)n = a

## SURDS AND INDICES -> EXAMPLES

1. What is the quotient when (x-1 - 1) is divided by (x - 1)? Sol. x-1 - 1 / x-1 - (1/x)-1 / x-1 = (1-x)/x =(1-x)/x * 1/(x-1) = -1/x. Hence, the required quotient is - 1/x If 2x-1 + 2x+1 = 1280, then find the value of x Sol. 2x-1 + 2x+1 = 1280 ⇔ 2x-1(1+2x) = 1280 ⇔ 2x-1 = 1280/5 = 256 = 28 ⇔ x-1 = 8 ⇔ x = 9. Hence, x = 9. If [1/5]3y = 0.008, then find the value of (0.25)y Sol. [1/5]3y = 0.008 = 8/1000 = 1/125 = [1/5]3 ⇔ 3y = 3 ⇔ y = 1. ∴ (0.25)y = (0.25)1 = 0.25. Hence, the required distance is 6 km.

## SURDS AND INDICES -> EXERCISE

1. The value of (256)5/4 is:

• A. 11 hrs 562 min
• B. 3 hrs 860 min
• C. 7 hrs 1020 min
• D. 7 hrs 1024 min
 Ans: D. Sol. (256)5/4 = (44)5/4 = 4(4*5/4) = 45 = 1024.

2. If 5a= 3125, then the value of 5(a-3) is

• A. 25
• B. 50
• C. 250
• D. 300
 Ans: A. Sol. 5a = 3125 = 5a = 55 a = 5. 5(1-3) = 5(5-3) = 52 = 25.

3. The value of 51/4 * (125)0.25 is:

• A. 5
• B. 55
• C. 5√5
• D. 5
 Ans: A. Sol. 51/4 * (125)0.25 = 50.25 * (53)0.25 * 5(3*0.25) = 50.25 * 50.75 = 5(0.25 + 0.75) = 51=5.