How to Solve Surds and Indices Problems

Dear Readers,

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

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) 5⁴

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

So, answer is option e.

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

Thanks.