## 4 Solved Surds And Indices Problems To Practice For IBPS PO Exam

Below are four problems based on surds and indices dealing with the calculations of index of numbers.

Question 1

Evaluate 360.14 x 12960.18

a) 12 b) 36 c) 6 d) 3

Solution :

Given that 360.14 x 12960.18
360.14 x (362)0.18
360.14 x 360.36
36(0.14 + 0.36) (Since ab x ac = a(b+c))
360.5
36(1/2)
sqrt(36)
6.

Question 2

Evaluate 640.2 x 160.4 x 4(-0.9)

a) 2 b) 1 c) 4 d) 16

Solution :

Given that 640.2 x 160.4 x 4(-0.9)
(43)0.2 x (42)0.4 x 4(-0.9)
4(3 x 0.2) x 4(2 x 0.4) x 4(-0.9)
40.6 x 40.8 x 4(-0.9)
4(0.6 + 0.8 - 0.9)
4(1.4 - 0.9)
40.5
sqrt4
2

Question 3

Evaluate 49(1/2) + 343(-1/3)

a) 52/7 b) 50/7 c) 15/7 d) 24/7

Solution :

Given that, 49(1/2) + 343(-1/3)
(72)(1/2) + (73)(-1/3)
7(2 x 1/2) + 7(-3 x 1/3)
7 + 7(-1)
7 + 1/7 (by using the rule a(-b) = 1/(ab))
(49 + 1) / 7
50/7

Question 4

Evaluate 81(-1/2) - [-27(-4/3)]

a) 8/81 b) 4/9 c) 4/81 d) 26/27

Solution :

Given that 81(-1/2) - [-27(-4/3)]
(92)(-1/2) - [(-33)(-4/3)]
9(-2 x 1/2) - (-3)(-3 x 4/3)
9(-1) - (-3)(-4)
1/9 - 1/[(-3)4]
1/9 - 1/81
8/81