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 thatso if we multiply the denominator byit will be rational. if we multiply the demoniator bywe must also multiply the numerators byso that
- Fractional indices may be used to express roots.
- Make sure you can use your calculator to find powers and roots. Theor button allows you to find roots.
- When the powers are fraction , then we can compare the indices in following manner.
for example :find which is greather or
step-1 : find the L.C.M of the denominator of the fraction i.e 4,5 = 20
step-2 : find powers with the L.C.M OR = AND
step-3 : compare the result obtained in setp-2 : i.e as 32 < 81 we can say <