Lesson 69: Adding and Subtracting Radical Expressions — Practice Questions

1. 1. Simplify the expression completely: $8\sqrt{6} + 5\sqrt{6} - 2\sqrt{6} = \_\_\_$.

2. 2. Which expression is the simplified form of $5\sqrt{3k} + 8\sqrt{2m} - 2\sqrt{3k}$?

   • A. $11\sqrt{8km}$
   • B. $3\sqrt{3k} + 8\sqrt{2m}$
   • C. $7\sqrt{3k} + 8\sqrt{2m}$
   • D. $11\sqrt{3k+2m}$

3. 3. Simplify the expression by first simplifying the radicals: $2\sqrt{75} - 4\sqrt{3} = \_\_\_$.

4. 4. Which of the following expressions cannot be simplified further by combining terms?

   • A. $5\sqrt{7} + 9\sqrt{7}$
   • B. $10\sqrt{32} - 3\sqrt{2}$
   • C. $4\sqrt{5} + 6\sqrt{11}$
   • D. $8\sqrt{y} - 3\sqrt{y}$

5. 5. Simplify the following expression: $\frac{10\sqrt{5x}}{7} - \frac{4\sqrt{5x}}{7} + \frac{9\sqrt{2y}}{7} = \_\_\_$.

6. 6. Which of the following pairs contains like radicals?

   • A. $6\sqrt{5}$ and $5\sqrt{6}$
   • B. $9\sqrt{11}$ and $-2\sqrt{11}$
   • C. $3\sqrt{2}$ and $3\sqrt{7}$
   • D. $8\sqrt[3]{5}$ and $8\sqrt{5}$

7. 7. Simplify the expression by combining like radicals: $10\sqrt{3} + 5\sqrt{7} - 4\sqrt{3}$. The simplified form is ___.

8. 8. Which radical is a 'like radical' to $4\sqrt{m^2n}$? (Assume $m$ and $n$ are positive).

   • A. $4\sqrt{mn^2}$
   • B. $m\sqrt{4n}$
   • C. $-9\sqrt{m^2n}$
   • D. $4\sqrt[3]{m^2n}$

9. 9. Simplify the expression: $9\sqrt{2} - 4\sqrt{5} + 6\sqrt{2} + 7\sqrt{5}$. The simplified form is ___.

10. 10. Why can't the expression $8\sqrt{6} + 2\sqrt{11}$ be simplified further?

    • A. The coefficients are different.
    • B. The indices are different.
    • C. The radicands are different.
    • D. One term must be negative to combine.