1. Learn about different sets of numbers.
Tuesday, 13 November 2018Tuesday, 13 November 2018
Learn about different sets of numbers.
Practice manipulating expressions involving surds .
Learn how to rationalise the denominator.
Evaluate expressions involving indices.
Simplify algebraic expressions involving indices.
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2. Real Numbers
Rational Numbers
Natural Numbers
Irrational Numbers
Integers

3. Solve these equations and write down which set(s) the number is in.
3x = 7
x + 7 = 3
x + 3 = 7
x2 = 7
x2 = -1

4. We met surds when solving quadratic equations.
e.g. Find the roots of the equation
Solution:
Using the formula for :
Simplifying the surd:

5. Let’s see why the answers (1) and (2) are the same
Roots of Equations
Roots is just another word for solutions !
e.g. Find the roots of the equation
Solution: There are no factors, so we can either complete the square or use the quadratic formula.
Completing the square:
Using the formula:
Let’s see why the answers (1) and (2) are the same

6. The answers from the quadratic formula can be simplified:
We have
Numbers such as are called surds
However,
4 is a perfect square so can be square-rooted, so
We have simplified the surd
So,
2 is a common factor of the numerator, so

7. Exercise
Simplify the following surds:
Exercise 1A