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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.
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. $\begin{array}{ll}{\text { We write: }} & {\text { We say: }} \\ {n^{2}} & {n \text { squared }} \\ {n^{3}} & {n \text { cubed }} \\ {n^{4}} & {n \text { to the fourth power }} \\ {n^{5}} & {n \text { to the fifth power }}\end{array}$
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.
1.7: Radicals and Rational Expressions
https://math.libretexts.org/Courses/Reedley_College/College_Algebra_1e_(OpenStax)/01%3A_Algebra_Review/1.07%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/Prince_Georges_Community_College/MAT_1350%3A_Precalculus_Part_I/01%3A_Prerequisites/1.03%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.
1.3: Radicals and Rational Expressions
https://math.libretexts.org/Courses/Chabot_College/Chabot_College_College_Algebra_for_BSTEM/01%3A_Prerequisites/1.03%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.
1.4: Radicals and Rational Expressions
https://math.libretexts.org/Workbench/College_Algebra_2e_(OpenStax)/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/Mission_College/Math_001%3A_College_Algebra_(Kravets)/01%3A_Prerequisites/1.03%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.
1.4: Radicals and Rational Expressions
https://math.libretexts.org/Courses/Coastline_College/Math_C115%3A_College_Algebra_(Tran)/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.

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