Mastering the Quotient Rule and Square Root Simplification

This video tutorial explains the quotient rule for simplifying square roots and demonstrates its application through various examples. It covers both the direct and reverse application of the rule, providing insights into when and how to use it effectively. The tutorial also extends the concept to cube roots, emphasizing the importance of evaluating the numbers involved before applying the rule.

What does the quotient rule allow you to do with a fraction under a square root?

• Multiply the numerators and denominators

• Combine the fraction under a single square root

• Subtract the numerators and denominators

• Add the numerators and denominators

What is the simplified form of the square root of 18 divided by the square root of 2?

• Square root of 36

• Square root of 9

• 6

• 3

Why might it not make sense to combine the square root of 3/4 under a single radical sign?

• Because it simplifies to 1

• Because 3 and 4 are not perfect squares

• Because 4 does not divide into 3 nicely

• Because it results in a complex number

What is the simplified form of the square root of 36 divided by the square root of 25?

• 5/6

• 6/5

• 36/5

• 6/25

What should you do before deciding to use the quotient rule?

• Check if the numbers are perfect squares

• Combine the radicals immediately

• Separate the radicals immediately

• Look at the numbers and see what makes the most sense

How do you simplify 2 times the square root of 50 over the square root of 2?

• 2 times the square root of 25

• Square root of 50

• 2 times the square root of 100

• Square root of 25

What is the simplified form of 3 times the square root of 49 over 81?

• 3 times 49/81

• 7/3

• 3 times 7/9

• 21/9

What is the cube root of 16 over the cube root of 2?

• 4

• 2

• Cube root of 32

• Cube root of 8

What is the simplified form of the cube root of 125 over 27?

• 5/27

• 125/3

• 5/3

• 3/5

Which of the following is a perfect cube?

• 81

• 49

• 27

• 16