Square Roots
What is √49?
7
What is ∛27?
3
Solve x² = 25. Find every solution.
x = −5 or x = 5
Between which two consecutive whole numbers is √20?
4 and 5, because 16 < 20 < 25.
What is √144?
12
What is ∛216?
6
Solve x³ = 64.
x = 4
Between which two consecutive whole numbers is √45?
6 and 7, because 36 < 45 < 49.
Select all the perfect squares: 36, 50, 81, 100.
36, 81, and 100.
6² = 36, 9² = 81, and 10² = 100.
Which equation describes the volume of a cube with side length 7?
A. V = 7²
B. V = 7³
C. V = ∛7
B. V = 7³.
Its volume is 343 cubic units.
Select all values that solve x² = 64: −8, 8, 32, 64.
−8 and 8
A student says √90 is between 8 and 9. Explain the mistake.
It is between 9 and 10 because 81 < 90 < 100.
A square garden has an area of 196 square feet. What is the length of one side? Show how you know.
14 feet, because 14² = 196.
A cube has a volume of 512 cubic inches. How long is one edge?
8 inches, because 8³ = 512.
A student says x = 8 is the only solution to x² = 64. Explain the error.
x = −8 also works because (−8)² = 64.
A square has an area of 110 square units. Between which whole numbers is its side length?
10 and 11 units, because 100 < 110 < 121.