Surds & Indices - Introduction and Examples (with Solutions), Quantitative Aptitude Quant Notes | EduRev

Quantitative Ability for SSC CHSL

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Quant : Surds & Indices - Introduction and Examples (with Solutions), Quantitative Aptitude Quant Notes | EduRev

The document Surds & Indices - Introduction and Examples (with Solutions), Quantitative Aptitude Quant Notes | EduRev is a part of the Quant Course Quantitative Ability for SSC CHSL.
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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:

Surds & Indices - Introduction and Examples (with Solutions), Quantitative Aptitude Quant Notes | EduRev

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: 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
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

= 54 × ¼

= 5

So, answer is option e.

1. Laws of Indices:

  1. am x an = am +
  2. Surds & Indices - Introduction and Examples (with Solutions), Quantitative Aptitude Quant Notes | EduRev
  3. (am)n = amn
  4. (ab)n = anbn
  5. Surds & Indices - Introduction and Examples (with Solutions), Quantitative Aptitude Quant Notes | EduRev
  6. a0 = 1

2. Surds:

Let a be rational number and n be a positive integer such that a(1/n) =  Surds & Indices - Introduction and Examples (with Solutions), Quantitative Aptitude Quant Notes | EduRev

Then, a is called a surd of order n.

3. Laws of Surds:

Surds & Indices - Introduction and Examples (with Solutions), Quantitative Aptitude Quant Notes | EduRev

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