8th Grade Radicals & Inequalities: Formula Challenges

1. A square garden has an area of 144 square meters. What is the length of one side of the garden? (Use radicals to find your answer.)

• 14 meters

• 10 meters

• 16 meters

• 12 meters

2. If 3x + 5 = 20, rearrange the formula to solve for x. What is the value of x?

• 5

• 15

• 2

• 10

3. The length of a rectangle is 3 meters more than twice its width. If the width is w, express the length in terms of w and create an inequality if the perimeter must be less than 30 meters.

• L = 3w + 3; 8w < 32

• L = 2w + 3; 6w < 24 (or w < 4) for perimeter < 30 meters.

• L = 2w - 3; 6w < 18

• L = w + 3; 4w < 20

4. Simplify the expression: 2√18 + 3√2. What is the final simplified form?

• 6√2

• 5√2

• 9√2

• 8√2

5. A car travels at a speed of 60 km/h. Write an inequality to represent the time (t) it takes to travel a distance (d) of at least 120 km. Rearrange the inequality to solve for t.

• t >= 2

• t <= 2

• t = 2

• t < 2

6. If the expression 4√x + 2√x can be simplified, what is the simplified expression?

• 4√x + 4√x

• 6√x

• 8√x

• 2√x

7. A triangle has a base of b meters and a height of h meters. The area of the triangle is given by the formula A = 1/2 * b * h. Rearrange this formula to solve for h in terms of A and b.

• h = A / (2b)

• h = (2A) / b

• h = 2A + b

• h = A - (1/2 * b)

8. If the sum of two like terms is 12x + 8, what could the two terms be? Provide an example of two like terms that add up to this expression.

• 12x + 0

• 6x + 6x

• 10x + 2x and 5 + 3

• 4 + 8x

9. A rectangular pool has a length that is 4 meters longer than its width. If the width is represented by w, write an expression for the area of the pool and create an inequality if the area must be less than 100 square meters.

• 2w + 4 < 100

• w^2 - 4w < 100

• w^2 + 4w > 100

• w^2 + 4w < 100

10. Evaluate the expression 5√(16) - 3 when x = 4. What is the final value?

• 10

• 20

• 15

• 17