Mr. Kone Math Hub · Review sheet

Approximating Irrational Roots

Unit 1: The Number System & Roots · NY-8.NS.2, NY-8.EE.2

Notes

Squeeze theorem for Grade 8. To estimate √40, note 6² = 36 and 7² = 49. So 6 < √40 < 7. Since 40 is closer to 36 than to 49, √40 is a little more than 6.3.

Vocabulary

• perfect square: An integer that is the square of an integer.

Practice (no calculator unless marked)

1. What is the solution for x in the equation x³ = 125?
2. The area of a square-shaped garden is 324 square feet. What is the length, in feet, of each side of the garden?
3. What is the solution for x in the equation x³ = 125?
4. The area of a square-shaped garden is 324 square feet. What is the length, in feet, of each side of the garden?
5. What is the solution for x in the equation x³ = 125?
6. The area of a square-shaped garden is 324 square feet. What is the length, in feet, of each side of the garden?
7. What is the solution for x in the equation x³ = 125?
8. The area of a square-shaped garden is 324 square feet. What is the length, in feet, of each side of the garden?