# Surds and Indices

Friday 1st of January 2016

### Sharing is caring

Surds, any root of rational number which cannot be easily calculated is known as Surd.

#### Rules of Surds

1. ${\left(\sqrt[n]{a}\right)}^{n}=a$
2. ${\left(\sqrt[n]{a}\right)}^{m}=\sqrt[n]{{a}^{m}}$
3. $\sqrt[n]{ab}=\sqrt[n]{a}×\sqrt[n]{b}$
4. $\sqrt[m]{\sqrt[n]{a}}=\sqrt[mn]{a}$
5. $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$
6. $\sqrt{a}×\sqrt{b}×\sqrt{c}=\sqrt{abc}$

Indices, Let a be a real number amd m is a positive integer, then . This is read as 'a raise to power m'. Here,a is known as base and m is known as index.

#### Rules of Indices

1. ${a}^{m}×{a}^{n}={a}^{m+n}$
2. ${a}^{m}÷{a}^{n}={a}^{m-n}$
3. $\left({a}^{m}{\right)}^{n}={a}^{mn}$
4. ${\left(ab\right)}^{m}={a}^{m}×{b}^{m}$
5. ${\left(\frac{a}{b}\right)}^{m}=\frac{{a}^{m}}{{b}^{m}}$
6. ${a}^{0}=1$