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IntroductionPowers are used when we want to multiply a number by itself repeatedly. 1. PowersWhen we wish to multiply a number by itself we use powers, or
indices as they are also called. For example, the quantity 7×
7×7×7 is usually written as Example 6 2 Your calculator will be pre-programmed to evaluate powers.
Most calculators have a button marked 2. Square rootsWhen 5 is squared we obtain 25. That is 5 The reverse of this process is called finding a square root.
The square root of 25 is 5. This is written as Note also that when -5 is squared we again obtain 25, that is
(-5) In general, a square root of a number is a number which when squared gives the original number. There are always two square roots of any positive number, one positive and one negative. However, negative numbers do not possess any square roots. Most calculators have a square root button, probably marked An important result is that the square root of a product of two numbers is equal to the product of the square roots of the two numbers. For example More generally, However your attention is drawn to a common error which
students make. It is not true that Exercises 1. Without using a calculator write down the value of Find the square of the following: 3. Show that the square of Answers 1. 18, (and also -18). 2. a) 2, b) 12. 3. Cube roots and higher rootsThe cube root of a number, is the number which when cubed
gives the original number. For example, because 4 we know that the cube root of 64 is 4, written Higher roots are defined in a similar way: because 2 Exercises 1. Without using a calculator find Answers 1. a) 3, b) 5. SurdsExpressions involving roots, for example It is often possible to write surds in equivalent forms. For
example, Exercises 1. Write the following in their simplest surd form: 2. By multiplying numerator and denominator by Answers |