1. Surd Sums

2. Starter
Remember the rules with Surds. Any surd can be simplified by breaking it down as follows…
Find 2 numbers that multiply to give this, one of which is square √ √ 27
Find 2 numbers that multiply to give this, one of which is square 72 √ √ √ √ 9 3 4 18
The square number can be simplified
The square number can be simplified √ √ 3 3 2 18
But you can keep simplifying √ √ 2 9 2
2 lots of root 9 is equal to 6 √ 6 2

3. Surd Sums
The rules with surds are exactly the same as the rules for algebra which you are familiar with…
Algebra
Surds
3x + 2x = 5x
3√ √2 = 5√2
2x - 4y cannot be simplified
2√ √3 cannot be simplified
a x b = ab
√2 x √3 = √(2x3)

4. Surd Sums
Example Questions
√ √45
√ √9√5
√ √5
= 4√5

5. Surd Sums
Example Questions
√ √7
√4√ √7
2√ √7
= √7

6. Surd Sums
Example Questions
√ √72
√9√ √36√2
3√ √2
= 9√2

7. Surd Sums
Example Questions
√ √32
√25√ √16√2
5√ √2
= √2

8. Plenary
√ √27
√25√3
+ √9√3
5√ √3
8√3

9. Plenary √5 √5 √5
1√5
√2√10
√20
√4√5
2√5
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10. Summary We have recapped our knowledge of surds
We have seen that the rules are the same of those in algebra
We also know how to simplify sums involving different surds