Algebra 2 Radicals Rational Exponents Quiz

Contents

This algebra 2 radicals rational exponents quiz asks 10 multiple-choice questions on radicals and rational exponents, and each answer comes with a short explanation.

Try these ten multiple-choice questions on nth roots, rational exponents, simplifying radicals and radical equations. Each question has exactly one correct answer, and the explanation points out the mistake that the wrong choices come from.

Algebra 2Common Core: N-RN.A.1 · N-RN.A.2 · A-REI.A.2

🎯 Radicals and Rational Exponents – Algebra 2 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

What is the value of \(125^{2/3}\)?

A \(5\)

B \(25\)

C \(\frac{1}{25}\)

D \(10\)

Question 2

Which radical is equal to \(x^{3/5}\)?

A \(\sqrt[3]{x^{5}}\)

B \(3\sqrt[5]{x}\)

C \(\sqrt[5]{x^{3}}\)

D \(\sqrt[8]{x}\)

Question 3

Which is \(\sqrt{98}\) in simplest form?

A \(49\sqrt{2}\)

B \(2\sqrt{7}\)

C \(7\sqrt{14}\)

D \(7\sqrt{2}\)

Question 4

What is \(\sqrt[3]{-8}\)?

A \(-2\)

B \(2\)

C \(-4\)

D not a real number

Question 5

What is the solution set of the equation whose graphs are shown?

Graphs of \(y=\sqrt{x-1}\) and \(y=x-3\).

\(\sqrt{x-1}=x-3\)

A \(x=2\) only

B \(x=2\) and \(x=5\)

C \(x=5\) only

D no solution

Question 6

What is the exact length of the hypotenuse?

Not drawn to scale.

A \(9\)

B \(3\sqrt{3}\)

C \(\sqrt{15}\)

D \(3\sqrt{5}\)

Question 7

Simplify \(2\sqrt{12}+\sqrt{27}\).

A \(7\sqrt{3}\)

B \(3\sqrt{39}\)

C \(5\sqrt{3}\)

D \(7\sqrt{6}\)

Question 8

A cube has a volume of 24 cubic units. What is its exact edge length?

Not drawn to scale.

A \(3\sqrt[3]{2}\)

B \(2\sqrt[3]{3}\)

C \(2\sqrt{6}\)

D \(6\sqrt[3]{4}\)

Question 9

What is the value of \(16^{-3/4}\)?

A \(\frac{1}{8}\)

B \(8\)

C \(-8\)

D \(\frac{1}{12}\)

Question 10

Simplify \(\left(x^{2/3}\right)^{3/4}\) for \(x>0\).

A \(x^{17/12}\)

B \(x^{8/9}\)

C \(x^{2}\)

D \(x^{1/2}\)

🎉 Quiz complete!

0 / 10

How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Standards N-RN.A.1, N-RN.A.2 and A-REI.A.2: rational exponents, radical forms, and radical equations.
\(a^{m/n}=(\sqrt[n]{a})^{m}\): the denominator is the root index, the numerator is the power.
An odd root of a negative number is real (\(\sqrt[3]{-8}=-2\)); an even root of a negative number is not real.
Simplify by pulling out perfect powers: \(\sqrt{72}=6\sqrt{2}\) and \(\sqrt[3]{54}=3\sqrt[3]{2}\).
Squaring both sides can create extraneous solutions, so every answer must be checked in the original equation.