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A rational number is one that you can write exactly in the form | Key point} Pp q where p and q are integers, q#0 Numbers that you cannot write exactly in this form are irrational numbers. If you express them as decimals, they have an infinite number of non-repeating decimal places. Some roots of numbers are irrational, for example, V3 = 1.732... and {10 = 2.15443... are irrational numbers. Irrational numbers involving roots, W ory ,are called surds. You can use the following laws to simplify surds Vax./b = Jab Va_ fa a You usually write surds in their simplest form, with the smallest possible number written inside the root sign. if Ja and Vb cannot be simplified, then you cannot simplify You can simplify surds by looking at their factors. You should look for factors that are square numbers. Va+Vb or Va-Vb For example 80 = J16 x V5 = 4/5 fora#b Simplify these expressions. Show your working. a V7xv7 b V5xJ/20 ¢ xs d J80-J20. ee 63+ 1 Bol [25 a V7xJ7=7 b J5x./20 = 100 =10 “ena 4 @ 45-25-25 eo BVT +4V7=7N7 raya +5 [2-7/2 ssh Calculations are often more difficult if surds appear in the denominator. You can simplify such expressions by removing any surds from the denominator. To do this, you multiply the numerator and denominator by the same value to find an equivalent fraction with surds in the numerator only, This is easier to simplify. this process is called rationalising the denominator. E] Algebra 1 Surds 
