13.1- Introduction
Question 1 :The solution of 3x^{2}= 300 lies between two consecutive integers. Calculate the two integers ?
13.2- Factors and Multiples
Question 1 : Prove algebraically that 2.75 ̇converts to the fraction \(\frac{124}{45}\) ?
13.3- Powers and Roots
Question 1 : Put these numbers in order from smallest to largest :
8 ×10^{-4}; 4 ×10^{-2} ; 6 ×10^{-4}; 0.07
Question 2 : Calculate the value of \(3^6-\sqrt{841}\) ?
13.4- Surds
Calculate exactly with fractions, surds and multiples of π ; simplify surd expressions involving squares (e.g. \(\sqrt{12}\) = \(\sqrt{(4 × 3)}\) = \(\sqrt{4 × 3}\) = \(2\sqrt{3}\) and rationalise denominators
Surds are numbers left in ‘square root form’ (or ‘cube root form’ etc). They are therefore irrational numbers.
Addition and Subtraction of Surds
Adding and subtracting surds are simple- however we need the numbers being square rooted (or cube rooted etc) to be the same
Rationalising the Denominator
It is untidy to have a fraction which has a surd denominator. This can be ‘tidied up’ by multiplying the top and bottom of the fraction by a particular expression. This is known as rationalising the denominator, since surds are irrational numbers and so you are changing the denominator from an irrational to a rational number.
Question 1 : Calculate \(\sqrt{0.4444.......}\) ?
Question 2 : Simplify \(\sqrt{80} + \sqrt{2\frac{2}{9}}\) giving the answer as \(\frac{a\sqrt{5}}{b}\) ?
13.5- Summary and Review
Question 1 : a is a common factor of 72 and 120. b is a common multiple of 6 and 9 . Calculate the highest possible value of \(\frac{a}{b}\) ?
13.6- Assessment 13
Question 1 : Rationalise the denominator of the following : :
a) \(\frac{1}{\sqrt{2}}\)
b) \(\frac{1 +\sqrt{2}}{1 -\sqrt{2}}\)
Question 2 : Calculate \(\sqrt[3]{64 × 1000 }\) ?