Exploring Square Roots and Cube Roots

The video tutorial covers the concepts of square roots and cube roots, explaining the differences between squaring numbers with and without parentheses. It discusses the inverse relationship between squaring and taking square roots, highlighting the principal square root. The tutorial also covers cubing numbers and cube roots, emphasizing that cube roots cannot have negative solutions. It provides a list of the first ten perfect squares and cubes, and evaluates various squares, square roots, cubes, and cube roots. The video concludes with a practical application involving arranging students in a square formation.

What is the result of squaring -3 when the negative sign is inside parentheses?

• -9

• 6

• -6

• 9

Which of the following is the principal square root of 16?

• -4

• 4

• -8

• 8

What is the cube root of 8?

• 2

• 8

• 4

• 1

Can a cube root ever have a negative solution? Why or why not?

• No, because cube roots are always positive

• No, because a negative number cubed is negative

• Yes, because cube roots can be both positive and negative

• Yes, because a negative number cubed is positive

What is 5 squared?

• 10

• 15

• 25

• 20

What is 3 cubed?

• 9

• 243

• 27

• 81

What is the result of (-7) squared?

• 49

• 14

• -49

• -14

What is the square root of 81?

• 10

• 9

• 8

• 7

What is the cube root of 216?

• 6

• 5

• 4

• 7

How many students should be lined up in each row if 225 students need to be arranged in a square formation?

• 10

• 12

• 20

• 15