step 1 We know that we can write the square root of 45 broken down into its prime factors as 5 times 3

Simplify. √(45)

Name: Problem 3, Chapter 8: McDougal Littell Jurgensen Geometry : Student Edition 2000
Uploaded: 2019-10-12T00:40:43-08:00
Duration: 14 s
Channel: Amrita Bhasin
Description: Simplify. √(45)

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Key Concepts

Simplifying Radicals

Simplifying radicals involves rewriting a radical expression in its simplest form, which usually includes identifying and extracting any perfect square factors from the radicand. This process ensures that the expression is presented in a more manageable and compact form.

Perfect Squares

Perfect squares are numbers that result from an integer multiplied by itself. Identifying perfect squares within the radicand allows for factoring them out, which helps in simplifying square root expressions.

Properties of Square Roots

The properties of square roots, such as ?(ab) = ?a × ?b, are fundamental when simplifying radical expressions. These properties allow one to separate the radicand into factors, extract perfect squares, and simplify the overall expression.

Prime Factorization

Prime factorization is the process of breaking down a number into its prime factors. This method is crucial in simplifying radicals because it helps to identify combinations of factors that form perfect squares, allowing the radical to be simplified effectively.

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