Practice finding square roots and cube roots, using perfect squares and perfect cubes, and understanding roots in real-world and geometric contexts.
Read each problem carefully. Show your work in the space provided. Use exact answers when possible, and estimate when asked.
Finding roots and connecting them to powers
Math - Grade 6-8
- 1
Find the square root of 81. Explain how you know.
- 2
Find the cube root of 64. Explain how you know.
- 3
A square has an area of 49 square centimeters. What is the side length of the square?
- 4
A cube has a volume of 125 cubic inches. What is the length of one edge of the cube?
- 5
List all the perfect squares between 1 and 100, including 1 and 100.
- 6
List all the perfect cubes between 1 and 125, including 1 and 125.
- 7
Simplify: √144
- 8
Simplify: ∛216
- 9
Estimate √50 to the nearest whole number. Explain your reasoning.
- 10
Estimate ∛30 to the nearest whole number. Explain your reasoning.
- 11
Complete the pattern: 2 squared = 4, 3 squared = 9, 4 squared = 16, so √16 = ___. Explain the relationship.
- 12
A student says that √36 equals 18 because 18 plus 18 equals 36. Explain the mistake and give the correct answer.