Principal square root

Definition

The principal square root of a non-negative number is its non-negative square root. It is denoted as $\sqrt{x}$ where $x$ is the number.

5 Must Know Facts For Your Next Test

1. The principal square root of $x$ is written as $\sqrt{x}$ and is always non-negative.
2. For any non-negative number $x$, the principal square root satisfies $(\sqrt{x})^2 = x$.
3. $\sqrt{0} = 0$ because $0^2 = 0$.
4. The principal square root function is only defined for non-negative numbers in the set of real numbers.
5. $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ for all non-negative numbers $a$ and $b$.

Review Questions

• What is the principal square root of 25?
• Explain why the principal square root of a negative number is not defined in the set of real numbers.
• Simplify $\sqrt{16 \cdot 9}$ using properties of radicals.

Related terms

Square Root: A value that, when multiplied by itself, gives the original number. Square roots can be positive or negative.

Radical Expression: An expression that includes a radical symbol, which indicates a root extraction such as a square root or cube root.

Rational Exponent: An exponent that is a fraction, where the numerator indicates a power and the denominator indicates a root.