8th Grade Challenge: Simplifying Radicals & Like Terms

1. Simplify the radical expression: √(50) + √(18). What is the simplified form?

• 8√2

• 4√2

• 10√2

• 6√2

2. Identify the like terms in the expression: 3x + 5y - 2x + 7y. What are the like terms?

• The like terms are 3x and -2x, 5y and 7y.

• 5x and 7y

• -2y and 7x

• 3y and 5x

3. A rectangle has a length of (2√3 + 4) meters and a width of (√3 + 1) meters. What is the expression for the perimeter of the rectangle?

• 6√3 + 10

• 4√3 + 8

• 6√3 + 8

• 8√3 + 6

4. Create an inequality based on the statement: A student must score more than 75% on a test to pass. Let x represent the score. Write the inequality.

• x < 75

• x ≥ 75

• x > 75

• x = 75

5. Factor the polynomial: x² - 9. What are the factors?

• (x - 9)(x + 1)

• (x - 6)(x + 6)

• (x - 3)(x - 3)

• (x - 3)(x + 3)

6. Find the zeros of the function: f(x) = x² - 16. What are the zeros?

• The zeros are 4 and -4.

• 0 and 16

• 8 and -8

• 2 and -2

7. Rearrange the formula for the area of a triangle, A = 1/2 * base * height, to solve for height. What is the rearranged formula?

• height = A * base

• height = A / (1/2 * base)

• height = 2A / base

• height = 1/2 * A / base

8. If 2√(x + 3) = 8, what is the value of x after simplifying the radical?

• 13

• 5

• 10

• 0

9. Combine the like terms in the expression: 4a + 3b - 2a + 5b. What is the simplified expression?

• 2a + 5b

• 6a + 2b

• 4a + 3b

• 2a + 8b

10. A car travels at a speed of (3√2) km/h. If it travels for 2 hours, what is the expression for the distance traveled?

• 6√2 km

• 4√2 km

• 12 km

• 8 km