Square Roots and Factor Trees

This video tutorial demonstrates how to find the square roots of 225, 256, 20, and 40 using factor trees. The instructor explains the process of creating a factor tree, identifying prime factors, and applying the rule of extracting pairs from under the radical sign. Each example is broken down step-by-step, showing how to simplify the square root by using prime factorization. The video concludes with a summary of the methods used and encourages viewers to subscribe for more educational content.

What is the first step in finding the square root of 225 using a factor tree?

• Divide 225 by 5

• Divide 225 by 3

• Divide 225 by 9

• Divide 225 by 15

Which prime numbers are used in the factorization of 225?

• 5 and 7

• 2 and 3

• 7 and 11

• 3 and 5

How many pairs of twos are there in the factorization of 256?

• One pair

• Two pairs

• Four pairs

• Three pairs

What is the square root of 256?

• 12

• 14

• 16

• 18

What is left under the radical sign after simplifying the square root of 20?

• 2

• 5

• 10

• 15

What is the exact square root of 20 expressed in simplest radical form?

• 2√2

• 2√3

• 2√5

• 2√10

What is the first step in creating a factor tree for 40?

• Divide 40 by 4

• Divide 40 by 5

• Divide 40 by 3

• Divide 40 by 2

What is the square root of 40 in simplest radical form?

• 8√5

• 6√5

• 4√5

• 2√5

What is the product of the numbers left inside the radical sign for the square root of 40?

• 15

• 20

• 10

• 5

What is the main purpose of using a factor tree in finding square roots?

• To divide the numbers

• To identify prime factors

• To find the sum of the numbers

• To multiply the numbers