Lesson 1: From Squares to Square Roots — Practice Questions

1. 1. What is the value of the expression $\sqrt{11^2}$? The value is ___.

2. 2. Calculate the value of $\sqrt{(-9)^2}$. The result is ___.

3. 3. For which values of the variable $a$ is the equation $\sqrt{a^2} = a$ always true?

   • A. For all real numbers $a$
   • B. Only when $a > 0$
   • C. Only when $a \geq 0$
   • D. Only when $a < 0$

4. 4. Which of the following expressions is equivalent to $\sqrt{(-15)^2}$?

   • A. -15
   • B. 15
   • C. 225
   • D. -225

5. 5. Simplify the expression: $\sqrt{10^2} + \sqrt{(-4)^2}$. The result is ___.

6. 6. Simplify the expression $\sqrt{5} \cdot \sqrt{10}$. The result is ___.

7. 7. Which expression is equivalent to $(3\sqrt{3})(2\sqrt{12})$?

   • A. 18
   • B. 36
   • C. $12\sqrt{3}$
   • D. $6\sqrt{15}$

8. 8. Simplify the expression $(\sqrt{8y})(\sqrt{2y^5})$. The simplified form is ___.

9. 9. Which expression is the result of simplifying $(\sqrt{12x})(\sqrt{3x})$?

   • A. 6x
   • B. 36x
   • C. $6x^2$
   • D. $\sqrt{15x^2}$

10. 10. Calculate the product of $(2\sqrt{6})(4\sqrt{15})$ and simplify completely. The result is ___.