Mastering Like Terms & Radical Expressions in Math

1. Sarah has 3x + 5y + 2x - 4y. What are the like terms and what is the simplified expression?

• 5x + y

• 3x + 9y

• 4x + y

• 6x - y

2. If the area of a square is represented by the expression x^2 + 4x + 4, what is the length of one side of the square after factoring?

• x + 4

• x + 2

• x + 1

• x + 3

3. A rectangle has a length of (2x + 3) meters and a width of (x + 1) meters. Write an expression for the perimeter and simplify it by combining like terms.

• 7x + 9

• 6x + 8

• 4x + 6

• 5x + 7

4. The sum of a number and its square is greater than 20. Write an inequality to represent this situation and solve for the number.

• x < -6 or x > 3

• x < -3 or x > 6

• x < -5 or x > 4

• x < -4 or x > 5

5. If 5√(x) + 3√(x) = 32, what is the value of x after simplifying the radical expression?

• 24

• 8

• 16

• 10

6. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write an inequality to represent the total cost if you want to spend no more than $100.

• 50 + 0.20m ≤ 100

• 50 + 0.20m = 100

• 50 + 0.20m < 100

• 50 + 0.20m ≥ 100

7. Simplify the expression 4√(16) + 2√(9) and provide the final answer.

• 18

• 24

• 20

• 22

8. If the formula for the volume of a cylinder is V = πr^2h, rearrange the formula to solve for h in terms of V and r.

• h = V / (πr^2)

• h = V / (2πr)

• h = πr^2V

• h = V / (r^2)

9. A gardener has 2x + 3y - 4x + 5y flowers. How many flowers does the gardener have after combining like terms?

• -2x + 8y

• -4x + 3y

• 2x + 5y

• -2x + 3y

10. If a triangle has sides represented by the expressions (3x + 2), (2x - 1), and (x + 5), write an inequality to show that the sum of the lengths of any two sides must be greater than the length of the third side.

• (3x + 2) + (x + 5) < (2x - 1)

• (3x + 2) + (2x - 1) > (x + 5), (3x + 2) + (x + 5) > (2x - 1), (2x - 1) + (x + 5) > (3x + 2)

• (3x + 2) + (2x - 1) < (x + 5)

• (2x - 1) + (x + 5) < (3x + 2)