Surds and Indices

Laws of Indices

Laws of Indices:

  • \(a^{m} \times a^{n}=a^{m+n}\)
  • \(\frac{a^{m}}{a^{n}}=a^{m-n}\)
  • \((a^{m})^n=a^{m n}\)
  • \((a b)^{n}=a^{n} b^{n}\)
  • \(\left(\frac{a}{b}\right)^{n}=\frac{a^{n}}{b^{n}}\)
  • \(a^{0}=1\)

SURDS

Surds: Let a be a rational number and n  be a positive  integer such that \(a^{\frac{1}{n}}=\sqrt[5]{a}\)  is irrational. Then, \(\sqrt[n]{a}\)  is called a surd of order n.

LAWS OF SURDS: 

  1. \(\sqrt[n]{a}=a^{\frac{1}{n}}\)
  2. \(\sqrt[n]{a b}=\sqrt[n]{a} \times \sqrt[n]{b}\)
  3. \(\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}\)
  4. \(\sqrt[m]{\sqrt[n]{\alpha}}=\sqrt[m n]{a}\)
  5. \((\sqrt[n]{a})^{n}=a\)
  6. \((\sqrt[n]{a})^{m}=\sqrt[n]{a^{m}}\)