Surds and Indices Questions Answers Formulas, Tips and Tricks

• 1. Laws of Indices

  
  

  $$\begin{aligned} i).& a^m \times a^n = a^{m+n} \\ ii).& \frac{a^m}{a^n} = a^{m-n} \\ iii).& (a^m)^n = a^{mn} \\ iv).& (ab)^n = a^n b^n \\ v).& \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \\ vi).& a^0 = 1 \\ \end{aligned}$$

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• 2. Surds formula

  
  

  Let a be a rational number and n be a positive integer such that $$\begin{aligned} a^{\frac{1}{n}} = \sqrt[n]{a} \end{aligned}$$ is irrational.
  
  then, $$\begin{aligned} \sqrt[n]{a} \end{aligned}$$ is called a surd of order n.

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• 3. Laws of Surds

  
  

  $$\begin{aligned} i.) & \sqrt[n]{a} = a^{\frac{1}{n}} \\ ii.) & \sqrt[n]{ab} = \sqrt[n]{a} * \sqrt[n]{b} \\ iii.) & \sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{ \sqrt[n]{b}} \\ iv.)& (\sqrt[n]{a})^n = a \\ v.)& (\sqrt[m]{\sqrt[n]{a}}) = \sqrt[mn]{a} \\ vi.)& (\sqrt[n]{a})^m = \sqrt[n]{a^m} \end{aligned}$$

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Surds and Indices Questions Answers