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Surds and indices is an important chapter that is often tested as part of the Quantitative Aptitude syllabus for government examinations such as SSC CGL, CHSL, CPO, MTS, Delhi Police, RRB NTPC and Railways. In this chapter, we will learn what surds and indices are, their formulas and practice the type of questions that you can expect in the examinations.

What are indices?

Indices are numbers that are raised to the power or exponent value of a number. If there is a number, say x, which has a power of y, then the number is xy. When we come across questions based on indices some basic formulas help us solve the expressions.

What are surds?

Surds are numbers that have fractional indices. Surds and indices are related via this rule;

xm/n=n√ xm

Laws of Indices:

In order to correctly solve questions tested from this topic, we must know and remember the laws that indices follow when different mathematical operations are in use. It must be remembered that the bases for all the indices are the same within 1 expression. The Laws of Indices are:

Multiplication: amxan= am+n

E.g., 59x 53= 53+9 =512

Division: am ÷ an= am-n

E. g., 59÷ 53= 59-3 =56

If a number has a power of power: (am)n= a mxn= amn

E.g., (59)3= 59x3 =527

If the power of any number is zero (0) then it is equal to 1: amxa0=am+0=am

E.g., 59x 50=59+0 =59 =59x1 59x 50=59x1 =1

When an exponent is raised to an exponent, they are multiplied: anm = a(nm)

E.g., 532 = 5(32) = 5(3⋅3) = 59 =1953125

When expressions involve perfect squares: n√p =p1/n

E.g., 1251/3 = 3√125 = 5

When exponents have negative powers: p-n = 1 / pn

E.g., 5-2 = 1/52 = 1/25 =0.04

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