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## Define rational and irrational numbers and perform operations with surds and fractional indices (ACMNA264)

[/title][fusion_text]LO: To define rational and irrational numbers and perform operations with surds and fractional indices.

Know:

• What is a rational number
• What is an irrational number
• How to complete the four basic operations
• What is a surd
• What is an indices

Understand:

• That certain numbers can’t be simplified to remove a square root and that operations can be used to solve problems involving surds.

Do:

• I can define rational and irrational numbers and perform operations with surds and fractional indices.

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# Examples (Visual Representations)

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# Notes

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## What are surds?

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## root5 = 2.2360679775. This is a surd because the result is not a rational number (the number goes on forever and doesn’t have an exact value).

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## Simplifying Surds

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### In the example to the left, we have the square root of 50. 50 can be broken down to 25 x 2. We know that the square root of 25 is 5 so we can move the 5 in front of the square root sign and we are left with the square root of 2 as a surd.

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## Multiplying Surds

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6. ### which leaves us with an answer of 30root11.

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### Same can be completed with subtraction.

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# Student Exemplars

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## Vibu and Rish Power Point

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# Practice Questions

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## My Maths 10/10A

### pg. 135 Exercise 3F Q. 1-4

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