Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. - ∛5/8

Verified step by step guidance

1. Identify the expression: $-\frac{\sqrt[3]{5}}{8}$.
2. Recognize that the cube root of a fraction can be expressed as the cube root of the numerator divided by the cube root of the denominator: $-\frac{\sqrt[3]{5}}{\sqrt[3]{8}}$.
3. Simplify the cube root of the denominator: $\sqrt[3]{8}=2$, since $2^3=8$.
4. Rewrite the expression using the simplified denominator: $-\frac{\sqrt[3]{5}}{2}$.
5. The expression is now simplified to $-\frac{\sqrt[3]{5}}{2}$, which is the final form.

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots or cube roots. In this context, the cube root (∛) signifies the number that, when multiplied by itself three times, yields the original number. Understanding how to manipulate these expressions is crucial for performing operations like addition, subtraction, multiplication, and division.

Properties of Radicals

The properties of radicals include rules that govern how to simplify and combine radical expressions. For instance, the product rule states that the square root of a product is the product of the square roots, and the quotient rule states that the square root of a quotient is the quotient of the square roots. These properties are essential for simplifying expressions involving radicals.

Rationalizing Denominators

Rationalizing the denominator is a technique used to eliminate radicals from the denominator of a fraction. This is often done by multiplying the numerator and denominator by a suitable radical that will result in a rational number in the denominator. This concept is important for presenting answers in a standard mathematical form.