Here ‘a’ is called the base and ‘n’ is known as the index of the power. Basically it is an exponential expression.
Rules of Indices: -
Indices: - Any root of a non negative rational number, which can not be found or does not provide an exact solution. For example n√a
Here ‘a’ is called as radicand and ‘n’ is known as the order of surds. ‘n’ should be a natural number.
Note: - All surds are irrational number but all irrational number are not surds.
Order of the surds:
Note: -
a) Surds of 2nd order are known as quadratic surds.
b) Surds of 3rd order are known as cubic surds.
Rules of Surds: -
Type of Surds: -
Formulas/ Patterns Including Short Tricks:
1) Arrangement of surds in either increasing or decreasing order –
First of all, take the LCM of the denominator of the powers and use it to make them same and then solve it.Example: -
2) Calculation on indices/ surds to find the value of any expression –
In such questions, factorize the expression in the smallest possible number then solve the expression using the rules of surds/ indices.Example: -
3) Addition operation on surds –
In such questions, break the x into m (m + 1) form then answer would be (m + 1).
Example: -
4) Subtraction operation on surds –
In such questions, factorize the x into m (m + 1) form then ‘m’ would be the answer.
Example: -
5) Multiplication operation on surds –
In such questions, answer would be
Where n = number of time x is repeated.
Example: -
6) Rationalization on surds –
In this process, we convert the denominator of the surds into a rational number. For this we have to multiply both numerator and denominator of the surds with another surd and obtain rational number by applying formula (a + b) * (a – b) = (a2- b2)
Example: -
Find the value of
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