Principal square root

Definition

The principal square root of a non-negative number $a$ is the non-negative number $x$ such that $x^2 = a$. It is denoted as $\sqrt{a}$ and is always greater than or equal to zero.

5 Must Know Facts For Your Next Test

1. The principal square root of a number is always non-negative.
2. For any non-negative real number $a$, $\sqrt{a} \geq 0$.
3. The principal square root of zero is zero, i.e., $\sqrt{0} = 0$.
4. If $a$ is a perfect square, then $\sqrt{a}$ is an integer.
5. For any positive real number $a$, there are two square roots: the principal (positive) and the negative, but by convention, $\sqrt{a}$ refers to the principal one.

Review Questions

• What is the principal square root of 16?
• Is the principal square root ever negative?
• What does $\sqrt{25}$ simplify to?

Related terms

Square Root: A value that, when multiplied by itself, gives the original number. There are two square roots for any positive number: one positive (the principal) and one negative.

Radical: An expression that includes a root symbol ($\sqrt{}$), used to denote roots such as square roots or cube roots.

Rational Exponents: $Rational\ exponents$ represent powers in fractional form, where $\frac{m}{n}$ indicates taking the n-th root first and then raising it to the m-th power.