8th Grade Radicals & Inequalities Word Problem Challenge

1. A square garden has an area of 144 square feet. What is the length of one side of the garden? (Use radicals)

• 10 feet

• 14 feet

• 12 feet

• 16 feet

2. If 3x + 5 < 20, what is the range of values for x? (Solve the inequality)

• x > 5

• x = 5

• x < 10

• x < 5

3. The sum of the square roots of two numbers is 10. If one number is 4, what is the other number? (Translate the word problem)

• 64

• 16

• 49

• 36

4. A recipe requires 2√3 cups of flour. If you want to make half the recipe, how much flour do you need? (Rearranging formulas)

• 4√3 cups

• √6 cups

• 2 cups

• √3 cups

5. If 5y - 3 > 2y + 12, what is the solution for y? (Solve the inequality)

• y < 5

• y = 5

• y > 5

• y < 0

6. The length of a rectangle is 3 times its width. If the perimeter is 48 meters, what is the width? (Translate the word problem)

• 6 meters

• 4 meters

• 10 meters

• 8 meters

7. Simplify the expression: 4√2 + 3√2 - 2√2. What is the result? (Like terms)

• 4√2

• 3√2

• 5√2

• 6√2

8. A car travels at a speed of 60 miles per hour. How long will it take to travel a distance of 240 miles? (Rearranging formulas)

• 6 hours

• 3 hours

• 4 hours

• 2 hours

9. If the square root of a number is less than 5, what is the range of possible values for that number? (Create an inequality)

• x = 30

• x > 25

• x < 25

• x ≤ 20

10. The total cost of 3 books and 2 notebooks is $30. If each book costs $8, how much does each notebook cost? (Translate the word problem)

• $10

• $15

• $5

• 3