Question 1

Which of the following best describes the difference between solving $$x^2 = 36$ and x = 36$?

Accepted Answer

Solving $$x^2 = 36$ gives two solutions, while x = 36$ gives only one.

Question 2

For $$\sqrt{-8x} to be a $$real number, what must be true about $$x$$?

Accepted Answer

$$x$$ must be less than or equal to zero.

Question 3

Simplify $$\sqrt{25}. $$What is the result?

Accepted Answer

$$5$$

Question 4

Simplify $$\sqrt{-25}. $$What is the result?

Accepted Answer

Not a real number

Question 5

Simplify $$\sqrt[4]{81}. $$What is the result?

Accepted Answer

$$3$$

Question 6

Write $$\sqrt[3]{x^2$ y^2$}$$ using fractional exponents.

Accepted Answer

$$x^{2/3}$$ $$y^{2/3}$$

Question 7

Rewrite $$(x^2$$ + $$y^2$$)^{1/2}$ without fractional exponents.

Accepted Answer

$$\sqrt{x^2$ + y^2$}$$

Question 8

Simplify $$\frac{x^5$}{x$$^{500}$$}.$$

Accepted Answer

$$x^{-495}$$

Question 9

Simplify $$\frac{3a^2$}{2b^7$}.$$

Accepted Answer

$$\frac{3a^2$}{2b^7$}$$

Question 10

Distribute and simplify: $$2(x^3$$ + $$1)(x^3 - 1$$)$$.

Accepted Answer

$$2(x^6 - 1$$)$$

Question 11

Rationalize the denominator: $$\frac{3}{\sqrt{6}}.$$

Accepted Answer

$$\frac{3\sqrt{6}}{6}$$

Question 12

Solve for $$x$$: $$2x^2 + 2 = 4$.

Accepted Answer

$$x = 1, x = -1$$

Question 13

Which equation has solutions $$-3$$ and $$4$$?

Accepted Answer

$$x^2 - x - 12 = 0$

Question 14

Given the quadratic equation $$2x^2 + 7x + 6 = 0$, what is the value of the discriminant?

Accepted Answer

$$7^2 - 4$$ \cdot 2 \cdot 6 = 49 - 48 = 1$$

Question 15

What does it mean if the discriminant $$b^2 - 4ac$$ \u003c 0$$ for a quadratic equation?

Accepted Answer

There are no real solutions.

Question 16

Solve for $$s$$: $$-s - 3 = \frac{s - 5}{2}.$$

Accepted Answer

$$s = 1$$

Question 17

Which of the following is the correct solution to $$x^2 = -25$?

Accepted Answer

No real solution

Question 18

Simplify $$\sqrt{\frac{49}{25}}.$$

Accepted Answer

$$\frac{7}{5}$$

Question 19

If $$b^2 - 4ac = 0$ for a quadratic equation, what can you say about its solutions?

Accepted Answer

There is exactly one real solution.

Algebra Test 4 Study Guide – Step-by-Step Guidance

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