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Roots

The root $\sqrt[n]{a}$ is the number that gives $a$ when raised to the power $n$ . A root can always be written as a fractional exponent, and a negative exponent means the fraction is flipped.

\sqrt[n]{a} = a^{1/n}

root as a fractional exponent

\sqrt{ab} = \sqrt{a}\cdot\sqrt{b}

product rule for roots

a^{-n} = \frac{1}{a^n}

negative exponent

Symbols

$n$	degree of the root
$a$	radicand, the number under the root sign

Example

$\sqrt[3]{64}\cdot 4^{-1} = 4\cdot\frac{1}{4} = 1$ , since $4^3 = 64$ .

\sqrt{a+b} \neq \sqrt{a}+\sqrt{b}

- roots only split over multiplication and division.

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Part of Foundations of Mathematics: Powers, roots and scientific notation.