Cube Roots and Factorization Concepts

This video tutorial explains how to find the cube roots of numbers using factor trees. It begins with the cube root of 343, a perfect cube, and demonstrates the process of prime factorization to simplify it. The video then covers the cube roots of 192 and 128, which are not perfect cubes, showing how to handle such cases by identifying triplets of prime factors and simplifying the expression under the radical sign. The tutorial emphasizes the rule of pulling out triplets for cube roots and provides a step-by-step guide to solving these problems without a calculator.

What is the first step in finding the cube root of a number?

• Create a factor tree

• Divide the number by 3

• Multiply the number by itself

• Subtract 1 from the number

Which of the following is a perfect cube?

• 192

• 256

• 128

• 343

What is the cube root of 343?

• 6

• 8

• 7

• 5

How many times does the number 2 appear in the factorization of 192?

• 4

• 5

• 7

• 6

What remains under the radical sign when finding the cube root of 192?

• 2

• 3

• 4

• 5

What is the cube root of 192 expressed in simplest form?

• 3 cube root 4

• 5 cube root 2

• 4 cube root 3

• 2 cube root 3

How many times does the number 2 appear in the factorization of 128?

• 5

• 7

• 6

• 8

What remains under the radical sign when finding the cube root of 128?

• 3

• 2

• 5

• 4

What is the cube root of 128 expressed in simplest form?

• 3 cube root 4

• 5 cube root 2

• 4 cube root 2

• 2 cube root 3

What method is suggested for finding cube roots without a calculator?

• Using a division method

• Using a multiplication table

• Using a factor tree

• Using a calculator