Question 1

Which of the following numbers is a rational number?

Accepted Answer

$$0.09$$

Question 2

Given a cube with a volume of $$216\ 	ext{in}^3$$, what is the length of one edge of the cube?

Accepted Answer

$$6\ 	ext{in}$$

Question 3

Simplify $$\sqrt{256}.$$

Accepted Answer

$$16$$

Question 4

Which of the following is the correct simplification of $$\sqrt{44}$$?

Accepted Answer

$$2\sqrt{11}$$

Question 5

Evaluate $$(-4)^2.$$

Accepted Answer

$$16$$

Question 6

A student claims that $$\sqrt{xy^2$} = xy. Is $$this correct? If not, what is the correct simplification for positive $$x$$ and $$y$$?

Accepted Answer

$$y\sqrt{x}$$

Question 7

Simplify the expression $$\$$left(p^{-2}$$q^3$$\$$right)^2$.

Accepted Answer

$$p^{-4}q^6$

Question 8

Which is greater: $$\sqrt{70} or$$ $$5\sqrt{3}$$?

Accepted Answer

$$\sqrt{70}$$

Question 9

Evaluate $$0.81^{1/2}.$$

Accepted Answer

$$0.9$$

Question 10

A moose weighs $$550\ 	ext{kg}. $$Scientists use the formula $$d = 0.099m$$^{0.90}$$ to estimate the volume of water d$ (in liters) the moose drinks in a day, where m$ is the mass in kilograms. How much water does the moose drink in a day (rounded to the nearest liter)?

Accepted Answer

$$38$$ liters

Question 11

Which of the following is an irrational number?

Accepted Answer

$$\sqrt{17}$$

Question 12

If the volume of a cube is $$64\ 	ext{in}^3$$, what is the length of one edge?

Accepted Answer

$$4\ 	ext{in}$$

Question 13

Simplify $$\left(\dfrac{1}{16}\$$right)^{1/2}$$.

Accepted Answer

$$\dfrac{1}{4}$$

Question 14

Which of the following is equivalent to $$5^0$$?

Accepted Answer

$$1$$

Question 15

Which of the following is the correct simplification of $$\sqrt{75}$$?

Accepted Answer

$$5\sqrt{3}$$

Question 16

If $$x$$ and $$y$$ are positive, which of the following is equivalent to $$\sqrt{x^2$y}$$?

Accepted Answer

$$x\sqrt{y}$$

Question 17

Which of the following is the correct value of $$16^{1/2}$$?

Accepted Answer

$$4$$

Question 18

Which of the following is the correct simplification of $$\$$left(5^2$$\$$right)^3$$?

Accepted Answer

$$5^6$$

Question 19

Which of the following is the correct value of $$0^2$$?

Accepted Answer

$$0$$

Question 20

If $$V = s^3$ is the formula for the volume of a cube, and V = 125$$\ 	ext{in}^3$$, what is the value of s$?

Accepted Answer

$$5\ 	ext{in}$$

Fundamental Concepts of Algebra: Rational and Irrational Numbers, Exponents, and Radicals

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