Quiz about Solve Rational Radical Absolute Value

Question 1

17. A student solved the radical equation $$\sqrt[]{\left(x^2-5\right)^3}=8$$ , and was about to check for extraneous solutions, when they noticed an error in their work. Can you spot the error(s)?
SELECT ALL THAT APPLY

Accepted Answer

Step 2: The cubed root of 64 is 4, not 8.

Answer

Step 1: Squaring does not cancel a square root. Squaring and square-rooting are not inverse operations.

Answer

Step 3: We should add 5 to both sides of the equation, not subtract 5.

Answer

Step 4: Taking a square root, or any even root, does not require both the positive and negative root.

Answer

There is no error - the equation is solved correctly.

Question 2

Use the properties of exponents and radicals to simplify the expression. Write your answer as a radical expression and with positive rational exponents.

Accepted Answer

$$10x^{\frac{7}{6}}=10\sqrt[6]{x^7}$$

Answer

$$40x^{\frac{7}{6}}=40\sqrt[6]{x^5}$$

Answer

$$10x^{\frac{1}{3}}=10\sqrt[3]{x}$$

Answer

$$40x^{\frac{8}{3}}=\sqrt[3]{40x^8}$$

Answer

$$10x^{\frac{7}{6}}=\sqrt[7]{10x^6}$$

Question 3

which value(s) of x make the expression undefined?

Accepted Answer

$$x e-3,\ \frac{1}{2}$$

Answer

$$x e-\frac{1}{2},\ 3$$

Answer

$$x e\frac{1}{2},\ 3$$

Answer

$$x=-3,\ 2$$

Answer

$$x e-3,\ -2$$

Question 4

Subtract and simplify.

Accepted Answer

Question 5

Solve the equation.

Accepted Answer

-29

Accepted Answer

25

Answer

-3

Answer

3

Answer

92/3</

Question 6

Solve the equation.

Accepted Answer

16

Answer

-16

Answer

8

Answer

-8

Answer

32

Question 7

Rationalize the denominator using the conjugate.

Accepted Answer

$$\sqrt[]{x}+\sqrt[]{3}$$

Answer

$$\frac{\left(x-3\right)\left(\sqrt[]{x}+\sqrt[]{3}\right)}{\left(x+3\right)}$$

Answer

$$\left(x-3\right)$$

Answer

$$\frac{\left(x-3\right)\left(\sqrt[]{x}+\sqrt[]{3}\right)}{x^2+9}$$

Question 8

Solve the absolute value equation. *Absolute Value means both the positive and negative!

CHOOSE ALL THAT APPLY

Accepted Answer

-3

Accepted Answer

9

Answer

6

Answer

-6

Answer

3

Question 9

What is the first step to solving Radical Equations?

Accepted Answer

Isolate the radical on one side of equations.

Answer

Check for extraneous solutions.

Answer

Raise each side of the equation to the power of the index.

Answer

Solve the remaining equation.

Answer

Convert from radical form to rational exponent form

Question 10

Question 10.

Accepted Answer

5

Answer

4

Answer

41

Answer

82

Question 11

Evaluate each expression.
| x + 9 | = -5

Accepted Answer

no solution

Answer

-14

Answer

-4

Answer

{-14, -4}

Question 12

Solve the absolute Value inequality and graph.

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 13

Write in radical form:

Accepted Answer

a.)

Answer

b.)

Answer

c.)

Answer

d.)

Question 14

Solve.

(Hint: isolate the radical)

Accepted Answer

45

Answer

55/3

Answer

5

Answer

189

Solve Rational Radical Absolute Value

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics