Math: Square Roots and Cube Roots
Finding roots and connecting them to powers
Math: Square Roots and Cube Roots
Finding roots and connecting them to powers
Math - Grade 6-8
- 1
Find the square root of 81. Explain how you know.
Think of a number that makes 81 when it is multiplied by itself.
The square root of 81 is 9 because 9 times 9 equals 81. - 2
Find the cube root of 64. Explain how you know.
Think of a number that is used as a factor three times to make 64.
The cube root of 64 is 4 because 4 times 4 times 4 equals 64. - 3
A square has an area of 49 square centimeters. What is the side length of the square?
The side length is 7 centimeters because the square root of 49 is 7. - 4
A cube has a volume of 125 cubic inches. What is the length of one edge of the cube?
For a cube, volume equals side length times side length times side length.
The edge length is 5 inches because the cube root of 125 is 5. - 5
List all the perfect squares between 1 and 100, including 1 and 100.
The perfect squares from 1 to 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. - 6
List all the perfect cubes between 1 and 125, including 1 and 125.
Use 1 cubed, 2 cubed, 3 cubed, and continue until you reach 125.
The perfect cubes from 1 to 125 are 1, 8, 27, 64, and 125. - 7
Simplify: √144
The value of √144 is 12 because 12 squared equals 144. - 8
Simplify: ∛216
Check 6 times 6 times 6.
The value of ∛216 is 6 because 6 cubed equals 216. - 9
Estimate √50 to the nearest whole number. Explain your reasoning.
Compare 50 to nearby perfect squares.
√50 is about 7 because 50 is between 49 and 64, and 50 is much closer to 49. Since √49 equals 7 and √64 equals 8, √50 rounds to 7. - 10
Estimate ∛30 to the nearest whole number. Explain your reasoning.
Compare 30 to nearby perfect cubes.
∛30 is about 3 because 30 is between 27 and 64, and 30 is much closer to 27. Since ∛27 equals 3 and ∛64 equals 4, ∛30 rounds to 3. - 11
Complete the pattern: 2 squared = 4, 3 squared = 9, 4 squared = 16, so √16 = ___. Explain the relationship.
√16 equals 4. Squaring 4 gives 16, and taking the square root of 16 reverses that operation. - 12
A student says that √36 equals 18 because 18 plus 18 equals 36. Explain the mistake and give the correct answer.
A root is connected to multiplication, not repeated addition.
The mistake is using addition instead of multiplication. A square root asks what number times itself equals 36, so √36 equals 6 because 6 times 6 equals 36.