Surds and Indices Shortcuts, Tricks, PDF and Formulas
Surds and Indices Points to Remember  Page 2
Surds and Indices Examples  Page 3
Surds and Indices Important Questions  Page 5
Important Formulas  Surds and Indices
 An integer is a whole number (positive, negative or zero). A rational number is one that can be expressed as a fraction , where a and b are integers. All integers, fractions and terminating or recurring decimals are rational.
 An irrational number cannot be expressed in the form , where a and b are integers. Examples of irrational numbers are .
 Real numbers are numbers that can be represented by points on the number line. Real numbers include both rational and irrational number.
 A surd is an irrational number involving a root. The numbers are examples of surds. Numbers such as are not surds because they are equal to rational numbers. =4 and root of ‘3’ or ‘root 3’. Note that we cannot take the square root of a negative number.
 Like surds involve the square root of the same number. Only like surds can be added or subtracted. For example, .
 Surds of the form can be simplified if the number beneath the square root sign has a factor that is a perfect square. For example, .
 The following rules can be used when multiplying or dividing surds.
 Rationalising the denominator of a surd means changing the denominator so that is a rational number. To rationalize the denominator of a surd such as we use the result that so if we multiply the denominator by it will be rational. if we multiply the demoniator by we must also multiply the numerators by so that
 Fractional indices may be used to express roots.
 Make sure you can use your calculator to find powers and roots. The or button allows you to find roots.
For example:
INDICES
 When the powers are fraction , then we can compare the indices in following manner.
for example :find which is greather or
step1 : find the L.C.M of the denominator of the fraction i.e 4,5 = 20
step2 : find powers with the L.C.M OR = AND
step3 : compare the result obtained in setp2 : i.e as 32 < 81 we can say <
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Comment made by Leah Wambui on Sep 30th 2018 at 5:47 pm:
help solve 5+2 root 6 all this into a square root =root2+root3
Comment made by Govind Singh on May 19th 2019 at 4:04 am:
nice pdf