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2021-11-03T14:32:47Z

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Lila: Created page with "The principal nth root of a is written as $\sqrt[n]{a}$ , where n is a positive integer greater than or equal to 2. In the radical expression, n is called the inde..."

2021-09-21T22:30:47Z

Created page with "The principal nth root of a is written as <math> \sqrt[n]{a} </math>, where n is a positive integer greater than or equal to 2. In the radical expression, n is called the inde..."

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The principal nth root of a is written as <math> \sqrt[n]{a} </math>, where n is a positive integer greater than or equal to 2. In the radical expression, n is called the index of the radical. Radical expressions can also be written without using the radical symbol. We can use rational (fractional) exponents. The index must be a positive integer, and if the index n is even, then a cannot be negative.

<math> \sqrt[n]{a} = a^{\frac{1}{n}} </math>

We can also have rational exponents with numerators other than 1. In these cases, the exponent must be a fraction in lowest terms. We raise the base to a power and take an nth root. The numerator tells us the power and the denominator tells us the root.

<math> a^{\frac{m}{n}} = (\sqrt[n]{a})^m = \sqrt[n]{a^m} </math>

All of the properties of exponents that we learned for integer exponents also hold for rational exponents.

==Resources==
* [https://www.khanacademy.org/test-prep/sat/sat-math-practice/new-sat-passport-advanced-mathematics/v/sat-math-p3-easier Radicals and rational exponents - Basic example], Khan Academy
* [https://openstax.org/books/college-algebra/pages/1-3-radicals-and-rational-exponents Radicals and Rational Exponents], OpenStax

← Older revision		Revision as of 14:32, 3 November 2021
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	* [https://www.khanacademy.org/test-prep/sat/sat-math-practice/new-sat-passport-advanced-mathematics/v/sat-math-p3-easier Radicals and rational exponents - Basic example], Khan Academy		* [https://www.khanacademy.org/test-prep/sat/sat-math-practice/new-sat-passport-advanced-mathematics/v/sat-math-p3-easier Radicals and rational exponents - Basic example], Khan Academy
	* [https://openstax.org/books/college-algebra/pages/1-3-radicals-and-rational-exponents Radicals and Rational Exponents], OpenStax		* [https://openstax.org/books/college-algebra/pages/1-3-radicals-and-rational-exponents Radicals and Rational Exponents], OpenStax
		+
		+	==Licensing==
		+	Content obtained and/or adapted from:
		+	* [https://openstax.org/books/college-algebra/pages/1-3-radicals-and-rational-exponents Radicals and Rational Exponents, OpenStax College Algebra] under a CC BY-SA license

Radical & Rational Exponent - Revision history

Lila: /* Resources */

Lila: Created page with "The principal nth root of a is written as \sqrt[n]{a} , where n is a positive integer greater than or equal to 2. In the radical expression, n is called the inde..."

Lila: Created page with "The principal nth root of a is written as $\sqrt[n]{a}$ , where n is a positive integer greater than or equal to 2. In the radical expression, n is called the inde..."