What Are They?
**Radicals** are expressions using a root symbol, like the square root $\sqrt{}$ or the cube root $\sqrt[3]{}$. They are the opposite of exponents. For example, $\sqrt{25}=5$ because $5^2=25$.
**Rational expressions** are expressions with fractional exponents. The numerator of the fraction is the power, and the denominator is the root.
The key relationship is: $$\sqrt[n]{x^m} = x^{m/n}$$
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Video: The Power of Radicals 🎬
This video will show you how radicals and rational exponents are related.
Practice Problems
Convert the following expressions and check your answers.
1) Write as a radical expression:
$$x^{1/2}$$
$$x^{1/2}$$
Answer:
2) Write with a rational exponent:
$$\sqrt[3]{y}$$
$$\sqrt[3]{y}$$
Answer:
3) Evaluate:
$$64^{1/3}$$
$$64^{1/3}$$
Value:
4) Evaluate:
$$\sqrt{81}$$
$$\sqrt{81}$$
Value:
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