Simplifying Roots and Exponents

This video tutorial covers simplifying radicals, including those with variables, and operations such as addition, subtraction, multiplication, and division. It explains rationalizing denominators and introduces imaginary numbers. The tutorial provides examples and practice problems to reinforce learning.

What is the largest perfect square that divides 50, allowing you to simplify the square root of 50?

• 16

• 9

• 4

• 25

Which of the following is a perfect cube that divides 54, allowing you to simplify the cube root of 54?

• 8

• 27

• 64

• 125

How do you simplify the expression 3√18 - 4√50 - 5√32?

• -25√2

• -19√2

• -29√2

• -31√2

What is the conjugate of the expression 5 + √3?

• 5 - √3

• √3 - 5

• 5 + √3

• √3 + 5

What is the simplified form of the expression 7 divided by the cube root of 4?

• 7√4

• 7/4

• 7√2

• 7/2

How do you express the square root of a negative number?

• As a complex number

• As an imaginary number

• As a rational number

• As a real number

What is the result of multiplying the cube root of 16 by the square root of 12?

• 4√6

• 4√5

• 4√3

• 4√2

What is the simplified form of the expression 3 divided by the ninth root of x^2 y^4 z^7?

• 3√x^2 y^5 z^7

• 3√x^5 y^7 z^2

• 3√x^7 y^5 z^2

• 3√x^7 y^2 z^5

What is the simplified form of the expression 5 divided by the seventh root of x^2?

• 5√x^3

• 5√x^2

• 5√x^7

• 5√x^5

What is the result of dividing the cube root of 32 by the fourth root of 32?

• 32^(1/3)

• 32^(1/4)

• 32^(1/12)

• 32^(1/6)