Evaluate each expression. (a) √(3) √(15) (b) (√(48))/(√(3)) (c) √(24) √(18)

Name: Problem 25, Chapter 1: Precalculus Mathematics for Calculus
Uploaded: 2020-05-29T15:14:54-08:00
Duration: 1 min 16 s
Channel: Bahar Tehranipoor
Description: Evaluate each expression. (a) √(3) √(15) (b) (√(48))/(√(3)) (c) √(24) √(18)

step 1 All right, so in this exercise, we want to evaluate these expressions that we're given and simpl

Evaluate each expression. (a) √(3) √(15) (b) ...

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Key Concepts

Simplification of Radical Expressions

Simplifying radical expressions requires identifying and extracting perfect power factors from under the radical sign. In the case of square roots, one looks for perfect squares, and in the case of cube roots, one seeks perfect cubes. This process reduces the radicands to simpler forms by rewriting them as products of perfect powers and other factors, ultimately leading to a simplified expression.

Operations with Radicals in Fractional Expressions

When radicals appear in fractions, properties of radicals allow the fraction to be rewritten by combining the square roots into one radical as long as they share the same index. This approach can simplify the expression by reducing it to a single radical that is easier to simplify further through extraction of perfect squares or cubes, consequently streamlining the evaluation process.

Properties of Radical Operations

This concept involves the fundamental properties of radicals, such as the product rule which allows you to combine radicals with the same index. Specifically, for nonnegative values, the property ?a · ?b = ?(ab) and its analogous property for cube roots, ??a · ??b = ??(ab), are used to simplify expressions. These rules are central to evaluating and simplifying expressions involving radicals.

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