# How to Solve Surds and Indices Problems Today I am teaching you the lesson that How to Solve Surds and Indices problems. 2-3 questions are asked from this chapter in various sections, i.e. Simplification, Approximation in Banking Exams as well as other general calculations in other exams.

### What are Surds?

The roots of those quantities which cannot be exactly obtained are called Surds.

Examples: √3, 2√5, 7√2

### What are Indices?

The expression 25 is defined as follows:
25 = 2 × 2 × 2 × 2 × 2

We call "2" the base and "5" the index.

### Shortcut to Remember Surds & Indices: Please go through these shortcuts. You have now learnt the important rules of the Law of Indices and are ready to try out some examples!

1. If √(X/0.0081) = ∛0.009 , the value of x is:
a) 0.729
b) 0.0729
c) 0.000729
d) 0.00729
e) None of these

### Solution:

√(X/0.0081) = ∛0.009
Or, √x/0.09 = ∛(9/1000)
Or, √x = 0.09 × 3/10
Or, √x = 0.027
Or, x = (0.027)2 = 0.000729

2. The value of √(9+ √(604+ √(424+ √(273+ √256) ) ) ) = ?
a) 8
b) 6
c) 5
d) 7
e) None of these

### Solution:

√(11+ √(604+ √(424+ √(273+ √256) ) ) )
= √(11+ √(604+ √(424+ √(273+ 16)) ) )
= √(11+ √(604+ √(424+ √289) ) )
= √(11+ √(604+ √(424+ 17)) )
= √(11+ √(604+ √441) )
= √(11+ √(604+ 21))
= √(11+ √625)
= √(11+ 25)
= √(11+ 25)
= √36
= 6

3. Simplification: 252.7 × 54.2 ÷ 55.4 = ?
a) 54
b) 53.2
c) 54.1
d) 54.2
e) None of these

### Solution:

252.7 × 54.2 ÷ 55.4
= 55.4 × 54.2 ÷ 55.4
= 55.4 × 54.2 ÷ 55.4
= 55.4 × 5-1.2
= 5(5.4 -1.2)
= 54.2

4. (625)0.16 × (625)0.09 = ?
a) 125
b) 25
c) 6.25
d) 12.5
e) 5

### Solution:

(625)0.16 × (625)0.09
= (625)0.16 + 0.09
= (625)0.25
= (625)1/4
= 54 × ¼
= 5

Hope this topic will help you to solve the Surds and Indices problems within in  1-2 minutes.

Thanks. 