## 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 36^{0.14} x 1296^{0.18}

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

**Answer :** c)6

Solution :

Given that 36^{0.14} x 1296^{0.18}

36^{0.14} x (36^{2})^{0.18}

36^{0.14} x 36^{0.36}

36^{(0.14 + 0.36)} (Since a^{b} x a^{c} = a^{(b+c)})

36^{0.5}

36^{(1/2)}

sqrt(36)

6.

Hence the answer is 6.

**Question 2**

Evaluate 64^{0.2} x 16^{0.4} x 4^{(-0.9)}

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

**Answer :** a) 2

Solution :

Given that 64^{0.2} x 16^{0.4} x 4^{(-0.9)}

(4^{3})^{0.2} x (4^{2})^{0.4} x 4^{(-0.9)}

4^{(3 x 0.2)} x 4^{(2 x 0.4)} x 4^{(-0.9)}

4^{0.6} x 4^{0.8} x 4^{(-0.9)}

4^{(0.6 + 0.8 - 0.9)}

4^{(1.4 - 0.9)}

4^{0.5}

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)}

(7^{2})^{(1/2)} + (7^{3})^{(-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/(a^{b}))

(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)}]

(9^{2})^{(-1/2)} - [(-3^{3})^{(-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.