# Nth roots and rational exponents

## Solved Exercises

Using Rational Roots. Although square roots are the most common rational roots, we can also find cube roots, 4th roots, 5th roots, and more. Just as the square.

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The "nth Root" used n times in a multiplication gives the original value. Instead of talking about the "4th", "16th", etc, if we want to talk generally we say the " n th ". So it is the general way of talking about roots so it could be 2nd, or 9th, or th, or whatever. This is the special symbol that means "nth root", it is the "radical" symbol used for square roots with a little n to mean nth root. It is an easy trap to fall into, so beware.

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## 7.1 nth Roots and Rational Exponents

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## 7.1/7.2 Nth Roots and Rational Exponents

Although square roots are the most common rational roots, we can also find cube roots, 4th roots, 5th roots, and more. Just as the square root function is the inverse of the squaring function, these roots are the inverse of their respective power functions. These functions can be useful when we need to determine the number that, when raised to a certain power, gives a certain number. We want to find what number raised to the 3rd power is equal to 8. Radical expressions can also be written without using the radical symbol. We can use rational fractional exponents. The index must be a positive integer.

This expression represents the result of multiplying the base , a , by itself as many times as the exponent , b , indicates. We read it as " a to the power of b ". In this page we are going to see cases where the exponent, b , is a fraction. In other words, we are going to work with roots and their powers. The number n is called the degree of the root and a is called the radicand of the root. Important: There are no roots with an even number degree 2, 4, 6, The product of two roots with the same degree is the root of same degree of the product of the radicands, this is,.

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nth roots and rational exponents

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