Exploring Square Roots and Cube Roots

The video tutorial covers the concepts of exponents, square roots, and cube roots. It begins with an introduction to bases and exponents, explaining how to express numbers in expanded form. The tutorial then explores square roots as inverse operations of squaring, providing examples and exercises. It continues with a discussion on cubes and cube roots, including a table of examples. The video also demonstrates solving equations using square and cube roots, emphasizing the importance of inverse operations. Finally, it applies these mathematical concepts to real-world scenarios, such as calculating the side length of a square and the volume of a cube.

What is the base in the expression 5^3?

• 25

• 15

• 5

• 3

How would you write the expression M^5 in expanded form?

• M^5

• 5M

• M * M * M * M * M

• M + M + M + M + M

What is the principal square root of 144?

• 18

• 16

• 14

• 12

If x^2 = 81, what is the value of x?

• 8

• 9

• 10

• 7

What is the cube root of 512?

• 9

• 8

• 7

• 6

Calculate the value of (-5)^3.

• 25

• 125

• -125

• -25

What is the cube root of 729?

• 9

• 10

• 8

• 7

If P^3 = 64, what is the value of P?

• 4

• 3

• 2

• 5

A square sign has an area of 900 square inches. What is the length of one side?

• 30 inches

• 35 inches

• 25 inches

• 20 inches

If the volume of a cube is 729 cubic inches, what is the length of one side?

• 7 inches

• 10 inches

• 8 inches

• 9 inches