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 $$\sqrt{54}$$?

Accepted Answer

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 $$\sqrt{12x^3$y^2$$}$?

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

Guida di studio - Domande di pratica

Study guide - Flashcard