Exploring Adding and Subtracting Rational Expressions

The video tutorial revisits square roots and cube roots involving variables. It begins with a refresher on square roots, explaining how to handle even and odd exponents. The tutorial then provides examples using perfect squares to simplify expressions. The second part introduces cube roots, detailing how to manage exponents that are multiples of three, with examples to illustrate the process.

What is the rule for finding the square root of a variable with an even exponent?

• Divide the exponent by 2

• Subtract 1 from the exponent

• Multiply the exponent by 2

• Divide the exponent by 3

How do you handle the square root of a variable with an odd exponent?

• Divide the exponent by 3

• Subtract 1 from the exponent and place the leftover under the radical

• Multiply the exponent by 2

• Add 1 to the exponent

What is the square root of 9 K to the 10th?

• 9 K to the 10th

• 3 K to the 10th

• 9 K to the 5th

• 3 K to the 5th

How do you simplify the square root of 40 a to the 19th?

• 4 a to the 10th radical 10 a

• 2 a to the 10th radical 10 a

• 4 a to the 9th radical 10 a

• 2 a to the 9th radical 10 a

What is the square root of 63 B squared?

• 3 B radical 7

• 9 B radical 7

• 3 B squared radical 7

• 9 B squared radical 7

What is the rule for finding the cube root of a variable with an exponent that is a multiple of three?

• Multiply the exponent by 3

• Divide the exponent by 3

• Subtract 1 from the exponent

• Divide the exponent by 2

How do you handle the cube root of a variable with an exponent that is not a multiple of three?

• Subtract 1 from the exponent

• Multiply the exponent by 3

• Divide the exponent by 2

• Break it apart so that part of it is a multiple of three

What is the cube root of 64 M to the 9th?

• 4 M cubed

• 8 M cubed

• 4 M to the 9th

• 8 M to the 9th

How do you simplify the cube root of P to the 7th?

• P squared radical P

• P to the 6th radical P

• P cubed radical P

• P to the 7th radical P

What is the cube root of 512 X Y to the 10th?

• 8 Y squared times the cubed root of X

• 8 Y squared times the cubed root of XY

• 8 Y cubed times the cubed root of X

• 8 Y cubed times the cubed root of XY