# Surds and Indices questions PDF Download for SSC CGL Exam

## Surds and Indices questions PDF Download for SSC CGL Exam

**Surds and Indices questions for ssc cgl pdf - Click Here to Download**

**Surds and Indices Concept**

Before solving the numerical on this chapter make sure that you are perfect with the chapter of square and square roots, simplification, linear and quadratic equations and decimal fractions.

**Important Terms**

**Surd:**Number which cannot be expressed in the fraction form of two integers is called as surd. Hence, the numbers in the form of 3,

^{3}2, …….

^{n}x

For example: | 1 | can be written as | 1 | but 3 cannot be written in the form of fraction |

9 | 3 |

**Indices:**Indices refers to the power to which a number is raised. Index is used to show that a number is repeatedly multiplied by itself.

For example: a

^{3}is a number with an index of 3 and base ‘a’. It is called as “a to the power of 3”

**Quick Tips and Tricks**

**1) The laws of indices and surds are to be remembered to solve problems on surds and indices.**

**Laws of Indices**

1) x

^{m}× x

^{n}= a

^{m+n}

2) (x

^{m})

^{n}= x

^{mn}

3) (xy)

^{n}= x

^{n}y

^{n}

4) | x^{m} |
= x^{m – n} |

x^{n} |

5) | x | ^{n} |
= | x^{n} |
||

y | y^{n} |

6) x^{–1} = |
1 |

x |

**Laws of Surds**

1)

^{n}x = x

^{(1/n)}

2)

^{n}xy =

^{n}x ×

^{n}y

^{n}(x/y) = |
^{n}x |

^{n}y |

^{n}x)

^{n}= X

5)

^{m}

^{n}x =

^{mn}x

6) (

^{n}x)

^{m}= (

^{n}x

^{m})

**2) Expressing a number in radical form**

Example: l x

^{(m/n)}l =

^{n}x

^{m}

The exponential form l x

^{(m/n)}l is expressed in radical form as

^{n}x

^{m}

**Important points to Remember**

**1)**Any number raised to the power zero is always equals to one. (Eg: x

^{0}= 1)

**2)**Surd

^{n}x can be simplified if factor of x is a perfect square

**3)**If denominator in a fraction has any surds, then rationalize the denominator by multiplying both numerator and denominator by a conjugate surd.

**4)**Every surd is an irrational number, but every irrational number is not a surd.

**5)**The conjugate of (2 + 7i) is (2 – 7i)

**6)**Different expressions can be simplified by rationalizing the denominator and eliminating the surd.

**Rationalizing the denominator:**

To rationalize the denominator 7 multiply with its conjugate to both numerator and denominator

Example 1: | 1 | = | 1 | × | 7 | = | 7 |

7 | 7 | 7 | 7 |

Example 2: | 1 | = | 1 | × | 7 – 3 | = | 7 – 3 |

7 + 3 | 7 + 3 | 7 – 3 | 4 |

Surds and Indices questions PDF Download for SSC CGL Exam
Reviewed by sscradar
on
July 09, 2019
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