Simplifying Radicals with Prime Factorization

The video tutorial introduces square roots, explaining the concept with simple examples like the square root of 9 and 100. It then delves into more complex square roots that result in non-whole numbers, using prime factorization to simplify them. The process of breaking down numbers into prime factors is demonstrated, showing how to simplify square roots by extracting perfect squares. The tutorial emphasizes understanding the underlying principles of square roots and prime factorization, providing a foundation for working with more complex mathematical problems.

What is the square root of 9?

• 5

• 4

• 3

• 2

Why is the square root of 100 equal to 10?

• Because 100 is an even number

• Because 10 times 10 equals 100

• Because 10 is a whole number

• Because 10 is a prime number

What does the square root operation ask?

• What number added to itself gives the number

• What number subtracted from itself gives the number

• What number divided by itself gives the number

• What number multiplied by itself gives the number

What is prime factorization?

• Dividing a number by its prime factors

• Breaking a number into its prime factors

• Adding a number to its prime factors

• Multiplying a number by its prime factors

What is the prime factorization of 92?

• 3 x 31

• 1 x 92

• 2 x 2 x 23

• 2 x 46

Which of the following numbers is prime?

• 100

• 46

• 23

• 92

What do you do when you reach a prime number in prime factorization?

• Add 1 to it

• Multiply it by 2

• Circle it

• Break it down further

How can 92 be written using its prime factors?

• 2 x 2 x 23

• 1 x 92

• 4 x 23

• 2 x 46

What happens when you have two of the same prime factors under a square root?

• You divide them

• You can pull one out of the square root

• You subtract them

• You add them

What is the square root of 4 times 23?

• 6

• 4

• 2

• 8