Radicals and Rational Exponents: Algebra 2 Math Test – PDF Download

Algebra 2 Radicals Rational Exponents Test: questions 1–5

Question 1: Roots and powers (2 points)

Evaluate each expression without a calculator.

1. \(\sqrt[3]{-125}\) (1 point)
2. \(81^{3/4}\) (1 point)

Question 2: Radical and exponent forms (2 points)

1. Write \(x^{5/3}\) as a radical. (1 point)
2. Write \(\sqrt[4]{y^{3}}\) with a rational exponent. (1 point)

Question 3: Simplify radicals (2 points)

Simplify each answer.

1. Find the exact length \(c\) of the hypotenuse of the triangle shown. (1 point)
2. Simplify \(\sqrt[3]{40x^{4}}\), where \(x\) is positive. (1 point)

Question 4: Combine radicals (2 points)

1. Simplify \(5\sqrt{12}-\sqrt{48}+\sqrt{75}\). (1 point)
2. Rationalize the denominator of \(\frac{12}{\sqrt{8}}\). (1 point)

Question 5: Exponent properties (2 points)

Simplify. Assume \(x\) and \(a\) are positive.

1. \(x^{2/3}\cdot x^{3/4}\) (1 point)
2. \((16a^{4})^{3/4}\) (1 point)

Algebra 2 Radicals Rational Exponents Test: questions 6–8

Question 6: Solve equations (3 points)

Solve each equation.

1. \(2\sqrt{3x-2}-4=6\) (1 point)
2. \(x^{3/2}=64\) (1 point)
3. \(\sqrt[3]{x+5}=-2\) (1 point)

Question 7: Extraneous solution (3 points)

The graphs of \(y=\sqrt{x+1}\) and \(y=x-1\) are shown.

1. Use the graph to estimate the solution of \(\sqrt{x+1}=x-1\). (1 point)
2. Solve the equation algebraically. (1 point)
3. Check each candidate and name any extraneous solution. (1 point)

Question 8: Cube-shaped box (4 points)

A cube-shaped gift box has a volume of \(192\) cubic inches.

1. Find the exact edge length in simplest radical form. (1 point)
2. Round the edge length to the nearest hundredth. (1 point)
3. Find the exact total surface area. (1 point)
4. The box must fit a shelf \(6\) inches high. Does it fit? Explain. (1 point)

How to use this algebra 2 radicals rational exponents test

Take this algebra 2 radicals rational exponents test without notes, then grade it with the test answer key out of 20 points.

Printable PDF · Test

Algebra 2 Radicals and Rational Exponents test

• 📄 US Letter
• 💾 172 KB
• 🖨️ Black and white friendly

Download the PDF

See every chapter on the Algebra 2 math page.

📘 The Mathovore bookAlgebra 2 Math Tests with Answer KeysA 45-minute test for every chapter

• 20 chapters in one PDF
• Tests scored out of 20 points
• Answer keys with scoring guides
• Perfect to prepare for exams

See the book →