Reducing Surds (Junior Cert Mathematics): Revision Notes

Reducing Surds

A surd is a number that has a square root that cannot be simplified into a whole number or a simple fraction.

• Non-Surds: $\sqrt{4} = 2$ (because it simplifies to a whole number) Surds are important in maths because they often show up in geometry, algebra, and other areas, so understanding how to work with them is essential.

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Three Important Rules for Surds

1. Adding and Subtracting Surds

• You can only add or subtract surds that have the same number inside the square root.

2. Multiplying Surds

• When you multiply surds, multiply the numbers inside the square roots together.

3. Dividing Surds

• When you divide surds, divide the numbers inside the square roots.

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Simplifying Surds

Simplifying a surd means breaking it down into a simpler form using the rules above.

Steps to Simplify a Surd:

4. Break Down the Number: Start by breaking the number inside the square root into factors (smaller numbers that multiply together to give the original number).
5. Look for Perfect Squares: Check if any of these factors are perfect squares (like $4, 9, 16, 25$), because you can simplify their square roots.

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Combining Simplified Surds

After simplifying surds, you can add or subtract them if they are the same type.

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Recap

• Simplifying surds helps make them easier to work with.
• Adding/subtracting is only possible when the numbers inside the square roots are the same.
• Multiplying/dividing surds is straightforward by applying the rules. With these notes, you now have a clear path to mastering surds. Keep practising to build your confidence and improve your skills!

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