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.

All you need of Quant at this link: Quant

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:

**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

√(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

√(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

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}

a) 125

b) 25

c) 6.25

d) 12.5

e) 5

(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.**

**1. Laws of Indices:**

*a*^{m}x*a*^{n}=*a*^{m +}- (
*a*^{m})^{n}=*a*^{mn} - (
*ab*)^{n}=*a*^{n}*b*^{n} *a*^{0}= 1

**2. Surds:**

Let *a* be rational number and *n* be a positive integer such that *a*^{(1/n)} =

Then, *a* is called a surd of order *n*.

**3. Laws of Surds:**

28 videos|20 docs|62 tests

### Surds & Indices - MCQ 1

- Test | 15 ques | 30 min

- Compound Interest - MCQ 4
- Test | 20 ques | 15 min
- Compound Interest - MCQ 3
- Test | 20 ques | 15 min
- Compound Interest - MCQ 2
- Test | 20 ques | 40 min
- Compound Interest - MCQ 1
- Test | 20 ques | 40 min