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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 Ability for SSC CHSL

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^-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.

1. Laws of Indices:

a^m x aⁿ = a^{m +}
(a^m)ⁿ = a^mn
(ab)ⁿ = aⁿbⁿ
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 Ability for SSC CHSL

Then, a is called a surd of order n.

3. Laws of Surds:

Surds & Indices - Introduction and Examples (with Solutions) | Quantitative Ability for SSC CHSL

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FAQs on Surds & Indices - Introduction and Examples (with Solutions) - Quantitative Ability for SSC CHSL

1. What is a surd?

Ans. A surd is an irrational number that cannot be expressed as a simple fraction. It is usually represented in the form √a, where a is a positive integer that is not a perfect square.

2. What is an index in surds and indices?

Ans. In surds and indices, an index refers to the power to which a number or variable is raised. For example, in the expression √a^3, the index is 3.

3. How do you simplify surds?

Ans. To simplify surds, you can factorize the number inside the surd and separate out any perfect square factors. Then, you can take the square root of the perfect square factors and leave the remaining factors inside the surd. For example, √12 can be simplified as 2√3.

4. What are the operations performed on surds?

Ans. The operations performed on surds include addition, subtraction, multiplication, and division. When performing these operations, it is important to simplify the surds and ensure that any resulting surds are in their simplest form.

5. How do you solve equations involving surds and indices?

Ans. To solve equations involving surds and indices, you can use the properties of indices to manipulate the equation and isolate the surd. Then, you can square both sides of the equation to eliminate the surd and solve for the variable. However, it is important to check for extraneous solutions, as squaring both sides of an equation can introduce additional solutions that may not be valid.

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