Simplify each expression. a. 5 √(10 x^2)-√(90 x^2) b. 8 √(27 x)-(1)/(2) √(64 x)

Name: Problem 102, Chapter 0: College Algebra: Real Mathematics, Real People
Uploaded: 2021-03-01T16:07:48-08:00
Duration: 2 min 10 s
Channel: Julie Silva
Description: Simplify each expression. a. 5 √(10 x^2)-√(90 x^2) b. 8 √(27 x)-(1)/(2) √(64 x)

step 1 We're being asked to simplify the two given expressions. So let's start with Part A. In this cas

Simplify each expression. a. 5 √(10 x^2)-√(90 x^2) b. 8 √(27...

Key Concepts

Combining Like Radical Terms

This concept involves adding or subtracting terms that contain the same radical part. Once the radicals are simplified and made uniform, similar terms can be combined together by adding or subtracting their coefficients, much like combining like terms in standard algebraic expressions.

Simplifying Radical Expressions

This concept refers to the process of rewriting expressions containing radicals into their simplest form. It involves factoring the number or variable inside the radical to identify perfect powers, and then extracting those factors from the radical sign. This simplification makes the expression easier to work with in further algebraic operations.

Properties of Radicals

Properties of radicals, such as the product rule (?(ab) = ?a?b for square roots and similarly for cube roots) and the division rule, are key to manipulating and simplifying radical expressions. They allow you to separate or combine radicals to facilitate extraction of perfect powers.

Extracting Perfect Powers

This involves identifying parts of the radicand that are perfect squares, cubes, or higher powers, which can then be taken outside the radical. Recognizing and extracting these perfect power factors is essential to simplifying radicals and reducing expressions to their simplest form.