Lesson Notes By Weeks and Term v4 - JHS 3

Lesson Video

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Performance objectives

• Define and differentiate between simple and compound surds.
• Simplify simple surds.
• Add, subtract, multiply, and divide simple surds.
• Apply knowledge of surds to solve problems.

Lesson summary

In our study of numbers so far, we have met whole numbers, integers, and fractions (rational numbers). However, in the real world, not all measurements are neat and tidy. Imagine finding the exact length of a diagonal line across a square classroom floor—the answer is often a number that cannot be written as a simple fraction. These numbers are called surds. Understanding surds is the first step towards solving more advanced problems in geometry, algebra, and even in careers like construction, engineering, and design. Today, we will learn to identify the two basic types of surds: simple and compound.

Lesson notes

Part A: What is a Surd?

First, let's remember what perfect squares are. They are numbers that result from multiplying an integer by itself. 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 4 x 4 = 16 ...and so on.

The square root of a perfect square is always a whole number. √4 = 2 √25 = 5 √100 = 10

These results (2, 5, 10) are rational numbers.