SURDS AND INDICES

Surd :-  Let a be a rational number and n be a positive integer. If the n th root of a is irrational, then

                                               $a^{\frac{1}{n}}=\sqrt[n]{a}$  is called a surd of order n.

             For eg.  $\sqrt{2}$, $\sqrt[4]{8}$, etc.

LAWS OF SURDS :-

1.   $\sqrt[n]{a}=a^{\frac{1}{n}}$

 

2.   $\sqrt[n]{ab}=\sqrt[n]{a}\times \sqrt[n]{b}$

 

3.   $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

 

4.   $(\sqrt[n]{a})^{n}=a$

 

5.   $\sqrt[m]{\sqrt[n]{a}}=\sqrt[mn]{a}$

 

6.   $(\sqrt[n]{a})^{m}=\sqrt[n]{a^{m}}$

LAWS OF INDICES  OR  EXPONENTS :-
                    For all real numbers a and b and positive integers m and n, we have

1.   $a^{m}\times a^{n}=a^{m+n}$

 

2.   $\frac{a^{m}}{a^{n}}=a^{m-n}$

 

3.   $(a^{m})^{n}=a^{mn}$

 

4.   $(ab)^{m}=a^{m}\times b^{m}$

 

5.   $(\frac{a}{b})^{m}=\frac{a^{m}}{b^{m}}$

 

6.   $a^{0}=1$