A free printable worksheet that pairs with the Rooted to the Spot game. The worksheet prints first, and the answer key prints on its own page after it, so you can leave it off. To make a PDF, click Print and choose "Save as PDF."

Penalty Kick Roots

Grade 8 · CCSS 8.EE.A.2, 8.NS.A.2 · Pairs with the Rooted to the Spot game

Name

Date

A square with an area of 49 has sides of 7, because 7 × 7 = 49. So √49 = 7. · ∛8 = 2 because 2 × 2 × 2 = 8.

Part A: Squares and square roots

1. 6² = ?

2. 12² = ?

3. √64 = ?

4. √169 = ?

Part B: Side of a square

5. A square rug has an area of 81 square feet. How long is each side?

feet

6. A square field has an area of 225 square meters. How long is each side?

meters

Part C: Estimate and cube roots

7. √30 is between which two whole numbers?

and

8. √90 is between which two whole numbers?

and

9. ∛27 = ?

10. ∛1000 = ?

11. Closer to which? √20 is between 4 and 5. Is it closer to 4 or to 5? Explain how you know.

12. Find the mistake. Jordan said √36 = 18 because 36 ÷ 2 = 18. What went wrong? What is √36 really?

Correct: √36 =

Answer Key: Penalty Kick Roots

For the teacher

6 × 6 = 36
12 × 12 = 144
8 (8 × 8 = 64)
13 (13 × 13 = 169)
9 feet (9 × 9 = 81)
15 meters (15 × 15 = 225)
5 and 6 (25 < 30 < 36)
9 and 10 (81 < 90 < 100)
3 (3 × 3 × 3 = 27)
10 (10 × 10 × 10 = 1000)
Between 4 and 5 (16 < 20 < 25). Closer to 4: 20 is 4 away from 16 but 5 away from 25. (√20 ≈ 4.47)
Jordan divided by 2 instead of finding the number that times itself makes 36. 6 × 6 = 36, so √36 = 6

#12 is the most common mistake: halving instead of undoing the square. In the game, a wrong answer draws the square as a grid so students can see that 6 rows of 6 make 36.