Roots and Radicals

Square Roots

• To create a square root symbol, simply use the \sqrt{} command.

  • Math inside the brackets are rendered as the radicand of the square root.

• f(x) = \sqrt{3x-5}

• x = {b \pm \sqrt{b^2 - 4ac} \over 2a}

• You can also nest square roots together.
  • \sqrt{ 3 + \sqrt{3 + \sqrt{ 3 + \sqrt{ 3 + \cdots }}}}

nth Order Roots

• Sometimes, we would also ask to display nth roots.
  • In this case, we add an optional argument \sqrt[]{} to indicate higher order roots:
  • Anything inside the square brackets gets displayed as the index of the root.

\sqrt[3]{32} = \sqrt[3]{2^3 \cdot 4} = 2 \cdot \sqrt[3]{4}