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

Dear Reader,
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

Answer : c)6

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.
Hence the answer is 6.

Question 2

Evaluate 640.2 x 160.4 x 4(-0.9)

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

Answer : a) 2

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
Hence the answer is 2.

Question 3

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

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

Answer : b)50/7

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
Hence the answer is 50/7.

Question 4

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

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

Answer : a)8/81

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
Hence the answer is 8/81.


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