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:

2

^{5}= 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) = ∛0.009Or, √x/0.09 = ∛(9/1000)

Or, √x = 0.09 × 3/10

Or, √x = 0.027

Or, x = (0.027)2 = 0.000729

**So, answer is option c.**

**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

**So, answer is option b.**

**3. Simplification: 25**

^{2.7}× 5^{4.2}÷ 5^{5.4}= ?
a) 5

^{4}
b) 5

^{3.2}
c) 5

^{4.1}
d) 5

^{4.2}
e) None of these

### Solution:

25

^{2.7}× 5^{4.2}÷ 5^{5.4}
= 5

^{5.4}× 5^{4.2}÷ 5^{5.4}
= 5

^{5.4}× 5^{4.2}÷ 5^{5.4}
= 5

^{5.4}× 5^{-1.2}
= 5

^{(5.4}^{-1.2)}
= 5

^{4.2}

**So, answer is option d.**

**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}
= 5

^{4 × ¼}
= 5

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

*Thanks.*
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