Simplify. √(147 m^7 n^11)

Name: Problem 85, Chapter 9: Elementary Algebra
Uploaded: 2021-07-16T15:59:05-08:00
Duration: 2 min 52 s
Channel: Chris Wojturski
Description: Simplify. √(147 m^7 n^11)

Key Concepts

Simplifying Radical Expressions

Simplifying radical expressions involves rewriting a radical (or square root) expression into its simplest form by extracting factors that are perfect squares or higher powers for other indices. The goal is to have no perfect square factors remaining under the radical, making the expression easier to work with interactively in further algebraic manipulations.

Exponent Rules in Radicals

When radicals contain variables with exponents, exponent rules help simplify the expression by separating the powers into even (or multiples of the index) and remaining parts. Specifically for square roots, any variable raised to an even power can be written as the square of another expression, allowing part of it to be taken out of the square root.

Perfect Square Identification

Identifying perfect squares is crucial in simplifying radicals. This includes recognizing numerical factors that are squares of integers as well as variable factors with exponents that are multiples of 2 in the case of square roots. Extracting these factors simplifies the expression by removing them from under the radical.

Multiplication Property of Radicals

The multiplication property of radicals states that the product of square roots can be consolidated into a single square root, and vice versa. This property is used to break down a complex radicand into components that can be simplified separately and then recombined, which is essential in the process of simplifying the overall expression.

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