Power, Indices and Surds Tips and Tricks
Table of Contents
In this article we will discuss about Surds & Indices. This topic are very useful and acts as the base of simplification and Algebra. It is compulsory that question will comes from this topic.
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Indices and Surds:
Let n be a positive integer and a be a real number, then :
where a^{n} is called “n^{th} power of a” or “a raised to the power n”
where, a is called the base and n is called index or exponent of the power a^{n}.
Laws of Indices:
- where and (m, n)
- (ab)^{n }= a^{n}b^{n}
- a^{p/q }=( a^{1/q })^{p} where p^{ }is a positive integer and q≠0
- If the index of a power is unit (i.e. 1) then the value of the power is equal to its base, i.e.
Surds:If a is rational and n is a positive integer and is irrational, then is called a surds of order n or nth root of a.
- A surd which has unity as its rational factor (i.e., a = 1) is called “pure surd”. e.g
- A surd which has a rational factor other than unity, the other irrational, is called “mixed surd”. e.g
Quadratic Surd:
A surd of order 2 (i.e ) is called a quadratic surd.
E.g. : is a quadratic surd but is not a quadratic surd because is a rational number. Therefore is not a surd.
Cubic Surd:
A surd of order 3 is called a cubic surd. e.g. 9^{1/3 }
Important Formulae Based on Surds :
Similar or like Surds:
surds having same irrational factors are called similar or like surds.
e.g.3√3, 4√3, 7√3 are similar surds.
Unlike surds:
Surds having no common irrational factors are called unlike surds.
e.g. 3√3, 7√5 are unlike surds.
Comparison of Surds:
If two surds are of the same order then the one whose radicand is larger is the larger surds.
7√3 > 3√3.
If two surds are of different order then:
Sol. Given surds are of order 2 & 3 respectively whose L.C.M. is 6.
Convert each into a surd of order 6, as shown below :
Some Useful Results :
therefor y=3
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