Question 1

Which of the following is the correct simplification of $\sqrt{50}$?

Accepted Answer

$\sqrt{50} = 5\sqrt{2}$

Question 2

A chemical solution requires the square root of 54 grams of a compound. What is the simplified form of $\sqrt{54}$?

Question 3

Which of the following is equivalent to $a^{\frac{3}{4}}$?

Accepted Answer

$\sqrt[4]{a^3}$

Question 4

Rationalize the denominator of $\frac{5}{\sqrt{3}}$.

Accepted Answer

$\frac{5\sqrt{3}}{3}$

Question 5

A rectangular box has a height of 9 cm, length $(x-12)$ cm, and width $(x-18)$ cm. If its volume is $144\ 	ext{cm}^3$, what is the value of $x$?

Accepted Answer

$x = 20$

Question 6

Which of the following is the correct solution to the quadratic equation $x^2 + 5x + 6 = 0$?

Accepted Answer

$x = -2$ or $x = -3$

Question 7

If $F = C + 32$ is the formula for converting Celsius to Fahrenheit, at what temperature are the Celsius and Fahrenheit readings the same?

Accepted Answer

$-40^\circ$

Question 8

Which of the following is the correct application of the product rule for radicals: $\sqrt{a} \cdot \sqrt{b}$?

Accepted Answer

$\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$

Question 9

Solve the equation $3x = 6(x-1)$ for $x$.

Accepted Answer

$x = 2$

Question 10

Which of the following is the correct solution to the quadratic equation $2x^2 + 5x + 3 = 0$?

Accepted Answer

$x = -1$ or $x = -3/2$

Question 11

Which of the following is the correct simplification of $\sqrt{12x^3y^2}$?

Accepted Answer

$2xy\sqrt{3x}$

Question 12

A total of $18,000 is invested, some in stocks and some in bonds. If the amount in bonds is half that invested in stocks, how much is invested in stocks?

Accepted Answer

$12,000$

Question 13

Which of the following is the correct form for expressing $a^{1/n}$ as a radical?

Accepted Answer

$a^{1/n} = \sqrt[n]{a}$

Question 14

Which of the following is the correct solution set for the equation $x^2 - 4 = 0$?

Accepted Answer

$x = 2$ or $x = -2$

Question 15

Which of the following is the correct way to rationalize the denominator of $\frac{3}{\sqrt{7} - \sqrt{2}}$?

Accepted Answer

$\frac{3(\sqrt{7} + \sqrt{2})}{5}$

Question 16

Which of the following is the correct solution to the equation quadratic in form: $u^2 + 3u - 10 = 0$?

Accepted Answer

$u = -5$ or $u = 2$

Question 17

Which of the following is the correct simplification of $\sqrt{8}$?

Accepted Answer

$2\sqrt{2}$

Question 18

If $a$ is a real number and $n$ is an odd integer, what is $\sqrt[n]{a}$?

Accepted Answer

$\sqrt[n]{a} = a$

Question 19

Which of the following is the correct solution to the equation $x^2 + 3x = 0$?

Accepted Answer

$x = 0$ or $x = -3$

Roots, Rational Exponents, and Equations: College Algebra Study Notes

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