EXPS 1 | Lesson 4 | Try This! (Simplify Radical Expressions)

The example below shows one method to simplify a radical expression by rewriting each root as an exponential expression and using the rules of exponents to simplify to an expression with one base and its exponent.

\(\sqrt x \cdot \sqrt {x^3} = x^{\frac12}\cdot x ^{\frac32}\), then \(x^{\frac12}\cdot x^{\frac32}=x^{\frac42}=x^2\)

Match each expression on the left to its simplified version on the right.

1. \(\sqrt[3]{x^2}\cdot \sqrt[3]{x^2}\)a. \(x^3\)
2. \(2\sqrt{x^3}\cdot\sqrt{x^5}\)b. \(2x^2\)
3. \(\sqrt x \cdot \sqrt[3]x\)c. \(2x^4\)
4. \((\sqrt{x^3})^2\)d. \(x^{\frac56}\)
5. \(\sqrt{2x^3}\cdot\sqrt{2x}\)e. \(x^{\frac43}\)

Answers : 1-e, 2-c, 3-d, 4-a, 5-b


Try This! (Solving Equations with Powers of 3)

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