Key Terms

index

$\sqrt[n]{a}$ n is called the index of the radical.

like radicals

Radicals with the same index and same radicand are called like radicals.

like square roots

Square roots with the same radicand are called like square roots.

nth root of a number

If $b^n=a$, then $b$ is an nth root of $a$.

principal nth root

The principal nth root of $a$ is written $\sqrt[n]{a}$.

radical equation

An equation in which the variable is in the radicand of a square root is called a radical equation

rational exponents

• If $\sqrt[n]{a}$ is a real number and $n\ge 2$, $a^{\frac{1}{n}}=\sqrt[n]{a}$.
• For any positive integers m and n, $a^{\frac{m}{n}}={\left(\sqrt[n]{a}\right)}^m$ and $a^{\frac{m}{n}}=\sqrt[n]{a^m}$.

rationalizing the denominator

The process of converting a fraction with a radical in the denominator to an equivalent fraction whose denominator is an integer is called rationalizing the denominator.

square of a number

• If $n^2=m$, then $m$ is the square of $n$

square root notation

• If $m=n^2$, then $\sqrt{m}=n$. We read $\sqrt{m}$ as ‘the square root of $m$.’

square root of a number

• If $n^2=m$, then $n$ is a square root of $m$