**SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Surds and Indices**

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In this chapter, we deals with questions based on index and surds of a number. Dealing with the topic candidate must have proper knowledge of basic concept and principle of surds and indices.

**Surds**

Any root of a rational number which cannot be exactly obtained is called a surd, e.g., √2, √6, √8, 3√4 etc.

**Order of Surds**

Let P be a rational number and m be a positive integer such that P^{1/m} = √P is irrational. Then, m√P is called surds of mth order.

e.g., 7½ = √7 = Surds of 2nd order.

**Some Important and Basic Rules of Surds**

**Method of Arranging Surds in Increasing or Decreasing Order**

Suppose given surds are p^{1/a}, q^{1/b} and r^{1/c}

First of all, take the LCM of a, b and c and use it to make the denominator of the powers the same. Then, easily we can find the required order.

**Example The greatest among the numbers 3√2, 3√7, 6√5, 2√20 is**

(a)3√2

(b)3√7

(c)6√5

(d)2√20

**Operations on Surds**

**Addition and Subtraction**

To add or subtract a surd, first make the possible factors of the terms, then add or subtract, i. e., Let x = √80 + 3√245 – √125

√80=√16 x 5=4√5; 3√245 =3√49×5=21√5; √125=√25×5=5√5 ,x=5√5

**Example If √18225 = 135, then the value of √18225 + √182.25 + √1.8225 + √0.018225 is SSC (10 + 2) 2012**

(a) 1.49985

(b) 14.9985

(c) 149.985

(d) 1499.85

**Multiplication and Division**

To multiply or divide the surds, we make the denominators of the powers same, then multiply or divide as usual –

i.e., Let x = √5 x 6√6 x 3√4

**Indices**

When a number ‘P’ is multiplied by itself ‘n’ times then the product is called nth power of ‘P and is written as P^{n}. Here, P is called the base an ‘n’ is known as the index of the power. (Here, plural of index is called indices)

**Some Important and Basic Rules of Indices**

**Essential Points**

**Reference Corner**

**1. If a ^{1/3} + b^{1/3} + c^{1/3} = 0, then a relation among a, b, c is SSC (10 + 2) 2014**

(a) a + b + c = 3abc

(b) a

^{3}+ b

^{3}+ c

^{3}= 0

(c) a + b + c=0

(d)(a + b+ c)

^{3}=27abc

**Answer:**

**2. If 3√a + 3√b = 3√c, then the simplest value of (a + b – c) ^{3} + 27abc is ssc (10+2) 2014**

(a) -3

(b) 0

(c) -1

(d) 3

**Answer:**

**3. Which one of the following is true? SSC (10+2) 2014**

(a) √5 + √3 > √6 +√2

(b) √5 + √3 < √6 +√2

(c) √5 + √3 = √6 +√2

(d)(√5 +√3)( √6 + √2)=1

**Answer:**

**4. Let 3√a = 3√26 + 3√7 + 3√63 . Then, SSC (10+2) 2013**

(a) a >729

(b)a = 729

(c) a <729 but a >216

(d)a<216

**Answer:**

**5. The value of (x ^{b+c}**

**)**

^{b-c}**(x**

^{c+a})^{c-a}(x^{a+b})^{a-b }(a)-1

(b)0

(c) 1

(d) 2

**Answer:**

**6. If x = √3 + √2 and y = √3 – √2, then the value of 8xy (x² + y²) is SSC (10 + 2) 2013**

(a) 16√6

(b)32

(c) 48√2

(d)80

**Answer:**

**Practice Exercise**

**Answers**

**Hints & Solutions**

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