1. Surds

2. Starter Simplify the following without a calculator a) b)
What does it mean to ‘simplify’ something in the above way?
 To write something equivalent, using smaller integer values

3. Surds
Any number that can be written as either an integer or a fraction is said to be rational
Eg) 2 is rational
0.5 is rational (1/2)
3.62 is rational (3 62/100 = 362/100)

4. Surds
Some numbers cannot be written as a fraction. As a decimal, they go on forever following a non-repeating pattern
π is irrational (3.1412……..)
So is √2 (1.412………)
So is √5 (2.236………)

5. Surds
To avoid rounding errors, we can leave some answers in ‘surd form’
This means we do not simplify to 2dp etc
Eg)
x² - 4 = 6
x² = 10
x = √10
(+4 to both sides)

6. Surds We can simplify some surds…. √20 √4 x √5  2 x √5  2√5
 2√5
(As 4 x 5 is 20)

7. Surds We can simplify some surds…. √18 √9 x √2  3 x √2  3√2
(As 9 x 2 is 18)

8. Surds Be careful… 3√5 is different to 3√5
This means ‘3 times the square root of 5’
This means ‘the cube root of 5’

9. Surds
Write the following as a whole number:
√3 x √12
 √36
 6

10. Surds
Write the following as a whole number:
√32 x √2
 √64
 8

11. Surds
Write the following as a whole number:
√20 ÷ √5
 √4
 2

12. Surds This process only works where all parts are Surds… √50 x √2
If both terms are Surds, they can be put together under the root sign…
√50 x √2
= √100
= 10
If one isn’t, simplify like in Algebra…
eg) 50 x a = 50a
50 x √2
= 50√2

13. Summary We have learnt what Surds are, and why they are used
We have seen how to ‘break up’ a Surd into 2 parts
We have also looked at putting a Surd ‘back together’