Simplifying Square Roots and Factor Trees

In this video, Brick Caspel explains how to write equivalent radical expressions, focusing on simplifying radicals using factor trees and recognizing perfect squares. The video covers examples from the Salvus Realize Algebra 1 textbook, demonstrating how to simplify the square roots of 63 and 44, and how to handle coefficients outside radicals. The instructor emphasizes understanding the process of factoring and simplifying, while also acknowledging alternative methods like using perfect squares.

What is the main goal of the video tutorial?

• To write equivalent radical expressions

• To compare different radical expressions

• To learn about algebraic fractions

• To solve linear equations

What is the first step in the factor tree method?

• Identify the perfect square

• Find the factor tree of the number under the radical

• Multiply the coefficients

• Divide the number by 2

What is the purpose of finding a factor tree?

• To identify perfect squares

• To simplify the expression under the radical

• To divide the number by 2

• To multiply coefficients

How is the square root of 63 simplified using the factor tree method?

• By recognizing it as a perfect square

• By dividing it by 2

• By expressing it as 7 times 9 and then 9 as 3 times 3

• By adding 7 and 9

What is the equivalent expression for the square root of 63?

• 9√3

• √63

• 7√3

• 3√7

What is the equivalent expression for the square root of 63 using the factor tree method?

• √63

• 9√3

• 7√3

• 3√7

What is a limitation of the perfect squares method?

• It requires a calculator

• It is too complex

• It doesn't work for any numbers

• It can miss multiple perfect squares

What is the first step in simplifying the square root of 44?

• Multiply by 2

• Find the factor tree

• Divide by 11

• Identify 4 as a perfect square

What is the simplified form of the square root of 44?

• √44

• 11√2

• 2√11

• 4√11

What is the simplified form of the square root of 44 using the perfect square method?

• 4√11

• 2√11

• √44

• 11√2