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

**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: **

Irrational numbers which contain the radical sign (√) are called as surds.

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

**For example:** a3 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## Laws of Surds## 2) Expressing a number in radical form
## 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.
- 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 |

- Numbers
- Highest Common Factor And Least Common Multiple
- Decimal
- Fractions
- Simplification
- Surds And Indices
- Chain Rule
- Square Root And Cube Root
- Ratio And Proportion
- Pipes And Cisterns
- Boats and Streams
- Problems on Trains
- Alligation or Mixtures
- Time and Distance
- Geometry
- Time and Work
- Simple Interest
- Problem Solving

- Business Administration Interview Questions and Answers
- Reading Comprehension
- What is a Function: Basics and Key Terms
- What is a CV?
- Time and Distance
- What Is a Number Line?
- Sentence Completion
- Statistical Officers Training Scheme (SOTS)
- NTS GAT Exam Day Tips
- General Knowledge
- Picture Pattern Series
- Capital Development Authority, Islamabad CDA Jobs
- Geometry
- How to Evaluate Reasoning
- Understanding Bar Graphs and Pie Charts

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