Surds Worksheets – New & Engaging

Surds Worksheets – New & Engaging

Surds Worksheets

Laws of Surds

Indices and Index Notation follow specific laws. Surds also have rules. The graphic below shows how to add, subtract and multiply surds.

Surds worksheet 1

What are Surds?

A surd is an irrational number - it cannot be written as the fraction a/b where a and be are integers. Surds are written with a √ symbol. √2 is a surd for example, expressed as “root 2”. The example below shows division rules for Surds such that √2 ÷ √3 is written as √2/√3. Notice that √2/√3 is not a fraction in the form a/b where a and b are integers - a whole number, and b is non-zero.

surds worksheet 3

The example below shows √3 ÷ √2.

surds worksheet 4In the example below shows √a + √a.

surds worksheet 5

The example below shows √5 + √5.

surds 6

Simplifying Surds

Just like simplifying expressions, Surds can be simplified. The rules are similar to collecting like terms. The question below shows 6√2 + 4√2.

simplifying surds 1

The question below shows √5 + 2√5 + 3√5.

simplifying surds 3

The question below shows √40 when simplified as a surd.

simplifying surds 4

The question below expands brackets when (√3 + 4)(√3 - 4). This technique is common when rationalising the denominator.

simplifying surds 5

Rational Numbers

The graphic below shows the real number system. The inner numbers include natural numbers including zero, integers which include negative numbers, rational numbers which include fractions, real numbers including surds and complex numbers.


Rational Numbers

For Substitution Cazoomy Worksheets try: Substitution Worksheets. For Trial And Improvement Cazoomy Worksheets try: Trial and Improvement Worksheets. For Simultaneous Equations Cazoomy Worksheets try: Simultaneous Equations Worksheets.