Adding and Subtracting Rational Expressions

This video tutorial covers dividing radicals and rationalizing the denominator. It begins with an introduction to dividing radicals, explaining the quotient rule and simplification process. The instructor then solves example problems, demonstrating how to apply these concepts. The tutorial transitions to rationalizing the denominator, explaining the process for both monomial and binomial denominators. Example problems are solved to illustrate the techniques, including multiplying by the conjugate for binomials.

What is the first step in dividing radicals?

• Multiply the coefficients

• Divide the coefficients

• Add the coefficients

• Subtract the coefficients

Using the quotient rule, what is the nth root of a over the nth root of b equivalent to?

• nth root of a minus b

• nth root of a times b

• nth root of a over b

• nth root of a plus b

What is the simplified form of 6 times the square root of 32?

• 30 square roots of 2

• 24 square roots of 2

• 12 square roots of 2

• 18 square roots of 2

What is the fourth root of 625?

• 5

• 6

• 4

• 3

What is the simplified form of 3 over 2 square roots of 5 after rationalizing the denominator?

• 3 square roots of 5 over 10

• 3 square roots of 5 over 5

• 3 square roots of 5 over 20

• 3 square roots of 5 over 15

What is the simplified form of the square root of 120 over 15?

• 2 square roots of 30 over 15

• 2 square roots of 15 over 15

• 2 square roots of 20 over 15

• 2 square roots of 25 over 15

What is the simplified form of 3 times the square root of 12 over 4 times the square root of 7?

• 3 square roots of 21 over 14

• 3 square roots of 21 over 21

• 3 square roots of 21 over 28

• 3 square roots of 21 over 7

What is the conjugate of 4 plus the square root of 2?

• 4 minus the square root of 3

• 4 plus the square root of 4

• 4 minus the square root of 2

• 4 plus the square root of 3

What is the simplified form of 16 minus 4 square roots of 2 all over 14?

• 8 minus 2 square roots of 2 over 7

• 8 minus 2 square roots of 2 over 28

• 8 minus 2 square roots of 2 over 14

• 8 minus 2 square roots of 2 over 21

What is the simplified form of 3 plus 4 square roots of 6 over negative 31?

• Negative 3 minus 4 square roots of 6 over 62

• Negative 3 plus 4 square roots of 6 over 62

• Negative 3 plus 4 square roots of 6 over 31

• Negative 3 minus 4 square roots of 6 over 31