Simplifying Square Roots and Factors

The video tutorial explains how to simplify expressions involving square roots by identifying perfect square factors and using prime factorization. It covers three examples: simplifying the square root of 192, simplifying 5√32 divided by 8, and simplifying 6 + 4√48 divided by 12. The tutorial emphasizes the importance of recognizing perfect squares and simplifying expressions step-by-step.

What is the first step in simplifying the square root of 192?

• Finding the cube root

• Determining the prime factorization

• Adding the numbers

• Subtracting the numbers

How many factors of 2 are there in the prime factorization of 192?

• Five

• Four

• Six

• Seven

What is the simplified form of √192?

• 10√3

• 6√3

• 8√3

• 4√3

What is the perfect square factor of 32 used in simplifying 5√32/8?

• 16

• 9

• 36

• 25

What is the simplified form of 5√32/8?

• 5√2/6

• 5√2/8

• 5√2/2

• 5√2/4

Why can't we simplify the 6 and 12 in the expression (6 + 4√48)/12?

• Because they are not divisible

• Because of the addition

• Because they are prime numbers

• Because they are even numbers

What is the perfect square factor of 48 used in simplifying (6 + 4√48)/12?

• 36

• 25

• 16

• 9

What is one way to simplify the expression (6 + 4√48)/12?

• By multiplying the numerator and denominator

• By factoring out a common factor

• By adding the terms

• By subtracting the terms

What is the simplified form of (6 + 4√48)/12?

• 3 + 8√3/6

• 3 + 4√3/6

• 3 + 8√3/3

• 3 + 4√3/3

What is another way to express (6 + 4√48)/12?

• 1/3 + 8√3/3

• 1/3 + 4√3/3

• 1/2 + 8√3/3

• 1/2 + 4√3/3