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1.4: Radicals and Rational Expressions
https://math.libretexts.org/Workbench/1250_Draft_3/01%3A_Prerequisites/1.04%3A_Radicals_and_Rational_Expressions
Just as we can rewrite the square root of a product as a product of square roots, so too can we rewrite the square root of a quotient as a quotient of square roots, using the quotient rule for simplif...Just as we can rewrite the square root of a product as a product of square roots, so too can we rewrite the square root of a quotient as a quotient of square roots, using the quotient rule for simplifying square roots. For a denominator containing the sum or difference of a rational and an irrational term, multiply the numerator and denominator by the conjugate of the denominator, which is found by changing the sign of the radical portion of the denominator.
5.7: Use Radicals in Functions
https://math.libretexts.org/Courses/Mission_College/Math_C%3A_Intermediate_Algebra_(Carr)/05%3A_Roots_and_Radicals/5.07%3A_Use_Radicals_in_Functions
In this section we will extend our previous work with functions to include radicals. If a function is defined by a radical expression, we call it a radical function.
8.3: Radicals and Rational Expressions
https://math.libretexts.org/Courses/Mission_College/Math_1X%3A_College_Algebra_w__Support_(Sklar)/08%3A_Support_Math_Topics/8.03%3A_Radicals_and_Rational_Expressions
Just as we can rewrite the square root of a product as a product of square roots, so too can we rewrite the square root of a quotient as a quotient of square roots, using the quotient rule for simplif...Just as we can rewrite the square root of a product as a product of square roots, so too can we rewrite the square root of a quotient as a quotient of square roots, using the quotient rule for simplifying square roots. For a denominator containing the sum or difference of a rational and an irrational term, multiply the numerator and denominator by the conjugate of the denominator, which is found by changing the sign of the radical portion of the denominator.
2.17: Simplifying Expressions with Roots
https://math.libretexts.org/Courses/Highline_College/MATHP_141%3A_Corequisite_Precalculus/02%3A_Algebra_Support/2.17%3A_Simplifying_Expressions_with_Roots
Remember that when a real number $n$ is multiplied by itself, we write $n^{2}$ and read it ' $n^{2}$ squared’. This number is called the square of $n$ , and $n$ is called the square root. \(\b...Remember that when a real number $n$ is multiplied by itself, we write $n^{2}$ and read it ' $n^{2}$ squared’. This number is called the square of $n$ , and $n$ is called the square root. $\begin{array}{ll}{\text { We write: }} & {\text { We say: }} \\ {n^{2}} & {n \text { squared }} \\ {n^{3}} & {n \text { cubed }} \\ {n^{4}} & {n \text { to the fourth power }} \\ {n^{5}} & {n \text { to the fifth power }}\end{array}$
5.3: Use Radicals in Functions
https://math.libretexts.org/Courses/Kansas_State_University/Your_Guide_to_Intermediate_Algebra/05%3A_Everything_else_you_need_to_know/5.03%3A_Use_Radicals_in_Functions
So, to find the domain of a radical function with even index, we set the radicand to be greater than or equal to zero. To graph the function, we choose points in the interval $[-3, \infty)$ that wil...So, to find the domain of a radical function with even index, we set the radicand to be greater than or equal to zero. To graph the function, we choose points in the interval $[-3, \infty)$ that will also give us a radicand which will be easy to take the square root. To graph the function, we choose points in the interval $(-\infty, \infty)$ that will also give us a radicand which will be easy to take the cube root.
1.4: Radicals and Rational Expressions
https://math.libretexts.org/Courses/Palo_Alto_College/College_Algebra/01%3A_Prerequisites/1.04%3A_Radicals_and_Rational_Expressions
Just as we can rewrite the square root of a product as a product of square roots, so too can we rewrite the square root of a quotient as a quotient of square roots, using the quotient rule for simplif...Just as we can rewrite the square root of a product as a product of square roots, so too can we rewrite the square root of a quotient as a quotient of square roots, using the quotient rule for simplifying square roots. For a denominator containing the sum or difference of a rational and an irrational term, multiply the numerator and denominator by the conjugate of the denominator, which is found by changing the sign of the radical portion of the denominator.
1.3: Radicals and Rational Expressions
https://math.libretexts.org/Courses/Hope_College/Math_125%3A_Hope_College/01%3A_Algebra_Essentials/1.03%3A_Radicals_and_Rational_Expressions
The principal square root of a is written as √a. The symbol is called a radical, the term under the symbol is called the radicand, and the entire expression is called a radical expression.
6.1: Simplify Expressions with Square Roots
https://math.libretexts.org/Courses/City_University_of_New_York/MAT1275_Basic/06%3A_Roots_and_Radicals/6.01%3A_Simplify_Expressions_with_Square_Roots
Remember that when a real number $n$ is multiplied by itself, we write $n^{2}$ and read it ' $n$ squared’. This number is called the square of $n$ , and $n$ is called the square root. If we wa...Remember that when a real number $n$ is multiplied by itself, we write $n^{2}$ and read it ' $n$ squared’. This number is called the square of $n$ , and $n$ is called the square root. If we want to find the negative square root of a number, we place a negative in front of the radical sign. The square root of a negative number is not a real number. We must use the absolute value signs when we take a square root of an expression with a variable in the radical.
4.10: Properties of Radicals and Simplifying Expressions Involving Roots
https://math.libretexts.org/Courses/Cosumnes_River_College/Corequisite_Codex/04%3A_Simplifying_Expressions/4.10%3A_Properties_of_Radicals_and_Simplifying_Expressions_Involving_Roots
Remember that when a real number $n$ is multiplied by itself, we write $n^{2}$ and read it ' $n^{2}$ squared’. This number is called the square of $n$ , and $n$ is called the square root. \(\b...Remember that when a real number $n$ is multiplied by itself, we write $n^{2}$ and read it ' $n^{2}$ squared’. This number is called the square of $n$ , and $n$ is called the square root. $\begin{array}{ll}{\text { We write: }} & {\text { We say: }} \\ {n^{2}} & {n \text { squared }} \\ {n^{3}} & {n \text { cubed }} \\ {n^{4}} & {n \text { to the fourth power }} \\ {n^{5}} & {n \text { to the fifth power }}\end{array}$
5.2: Radical Functions
https://math.libretexts.org/Courses/Fresno_City_College/Math_3A%3A_College_Algebra_-_Fresno_City_College/05%3A_Other_Functions/5.02%3A_Radical_Functions
In this section we will extend our previous work with functions to include radicals. If a function is defined by a radical expression, we call it a radical function.
17.2: Simplify Expressions with Roots
https://math.libretexts.org/Courses/Las_Positas_College/Foundational_Mathematics/17%3A_Radical_Expressions_and_Functions/17.02%3A_Simplify_Expressions_with_Roots
Remember that when a real number $n$ is multiplied by itself, we write $n^{2}$ and read it ' $n^{2}$ squared’. This number is called the square of $n$ , and $n$ is called the square root. \(\b...Remember that when a real number $n$ is multiplied by itself, we write $n^{2}$ and read it ' $n^{2}$ squared’. This number is called the square of $n$ , and $n$ is called the square root. $\begin{array}{ll}{\text { We write: }} & {\text { We say: }} \\ {n^{2}} & {n \text { squared }} \\ {n^{3}} & {n \text { cubed }} \\ {n^{4}} & {n \text { to the fourth power }} \\ {n^{5}} & {n \text { to the fifth power }}\end{array}$

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