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. "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

Real Numbers Rational Numbers Natural Numbers Irrational Numbers Integers

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

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

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

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

Exercise Simplify the following surds: Exercise 1A