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Important formulae :

a) Indices :

* a^{n} = a . a . a ......(n times)

* a^{m} . a^{n} . a^{p} = a^{m + n + ..... + p}

* a^{m} . a^{n} = a^{m + n}

*

* (a^{m})^{n }= a^{mn} = (a^{n})^{m}

* (ab)^{n} = a^{n}b^{n}

*

*

*

*

* where a ∈ r, a ≠ 0

*

* If a^{m} = a^{n} Where a ≠ 0, a ≠ ± 1 then m = n

* a^{n} = b^{n} Where n ≠ 0 then a = ± b

b) Surds :

Let 'a' be a rational number and 'n' be a positive integer such that is irrational. then is called surd of order 'n'.

i.e. → is a surd of order 7.

* Every surd is a irrational number.

Rules of surds :

*

*

* times =

*

* then p(p – 1) = a

* Conjugate surd :

* Condition of equality of surds

If

then a = c, b = d

To arrange the surds in increasing or decreasing order →

If the given surds are so the steps to be followed for comparison.

(i) First find the LCM of (m, n, p) order of surds.

(ii) Then the numerator and denominator of power is multiplied by such a number so that denominator of all terms becomes equal to the LCM.

Example :

Compare

LCM of (4, 3, 6) = 12

So,

= 27, 16, 25

So, order is ⇒