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
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 \(y=x-3\).
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!
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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.
See every chapter on the Algebra 2 math page.