Surds

• What are surds?

  Surds are square roots that cannot be reduced to rational numbers.
• Why is \(\sqrt{4}\) not considered a surd?

  Because \(\sqrt{4} = 2\), which is a rational number.
• What is an example of a surd?

  \(\sqrt{5}\) is an example of a surd.
• What happens when you use a calculator to find \(\sqrt{5}\)?

  You get an approximate value of \(2.236067977...\), which needs rounding.
• Why is it better to leave a surd in its exact form?

  Leaving it as a surd keeps the answer exact and avoids rounding errors.
• What are the general rules for simplifying expressions involving surds?


  • \(\sqrt{a} \times \sqrt{a} = a\)
  • \(\sqrt{ab} = \sqrt{a} \times \sqrt{b}\)
  • \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\)
• How do you simplify \(\sqrt{12}\)?

  \(\sqrt{12} = 2\sqrt{3}\)
• What is the simplified form of \(\sqrt{48}\)?

  \(\sqrt{48} = 4\sqrt{3}\)
• How do you simplify \(\sqrt{\frac{16}{9}}\)?


  \(\sqrt{\frac{16}{9}} = \frac{4}{3}\)
• What is the simplified form of \(\sqrt{8} + \sqrt{18} + \sqrt{50}\)?

  \(\sqrt{8} + \sqrt{18} + \sqrt{50} = 10\sqrt{2}\)
• What is the process for simplifying the expression \(\sqrt{8} + \sqrt{18} + \sqrt{50}\)?

  1. \(\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}\)
  2. \(\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}\)
  3. \(\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}\)
  4. Combine: \(2\sqrt{2} + 3\sqrt{2} + 5\sqrt{2} = 10\sqrt{2}\)