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Formulas for solving Problems on Surds and Indices - Aptitude Questions and Answers.

TIPS FOR SOLVING QUESTIONS RELATED TO SURDS AND INDICES:

1. 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} then, \begin{aligned} \sqrt[n]{a} \end{aligned} is called a surd of order n.

2. 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}

3. 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}