Properties of Absolute Value (Theorems)

According to the properties of absolute value, \(|a \cdot b|\) equals:

For \(b \neq 0\), \(\left|\dfrac{a}{b}\right|\) equals:

The Triangle Inequality states that \(|x + y|\) is:

For which of the following pairs does \(|a + b| = |a| + |b|\)?

Compute \(|3| \cdot |-5|\).

Compute \(|3| \cdot |-5|\).

Given \(b = -4\), compute \(|b|^2\).

Given \(b = -4\), compute \(|b|^2\).

The theorem \(\big||a| - |b|\big|\) states that this quantity is:

The general rule is that |a + b| is strictly less than |a| + |b| when:

For \(a \geq 0\), the symbol \(\sqrt{a}\) always denotes the ______ square root of a (never the negative one).

For \(a \geq 0\), the symbol \(\sqrt{a}\) always denotes the ______ square root of a (never the negative one).