1C - Irrational numbers
An irrational number is any number that cannot be expressed as a fraction of two integers (\(Z\)). Although there are many different irrational numbers, we will primarily look at surds in this section.
- Surds can be simplified by identifying perfect squares that are factors of the number under the radical sign.
1C - Example 1: Simplifying surds
Simplify each of the following
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1C - Example 1: Video solution
1C - Example 1: Practice
Question 1: ABC Question 2: ABC 1C - Example 1: Solutions
Question 1: ABC Question 2: ABC |
- Surds can only be added or subtracted when they contain the same irrational factor; that is, they are like surds.
- Often like surds can be identified by first simplifying.
1C - Example 2: Addition and subtraction of surds
Simplify each of the following
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1C - Example 2: Video solution
1C - Example 2: Practice
Question 1: ABC Question 2: ABC 1C - Example 2: Solutions
Question 1: ABC Question 2: ABC |
1C - Example 3: Addition and subtraction of surds
Simplify each of the following
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1C - Example 3: Video solution
1C - Example 3: Practice
Question 1: ABC Question 2: ABC 1C - Example 3: Solutions
Question 1: ABC Question 2: ABC |
- To rationalise the denominator, we multiply by a fraction equivalent to \(1\) which results in a rational number in the denominator. In some cases, the Difference of Perfect Squares (DOPS) pattern is required.
1C - Example 4: Rationalising the denominator
Simplify each of the following
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1C - Example 4: Video solution
1C - Example 4: Practice
Question 1: ABC Question 2: ABC 1C - Example 4: Solutions
Question 1: ABC Question 2: ABC |