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- https://math.libretexts.org/Workbench/1250_Draft_3/01%3A_Prerequisites/1.04%3A_Radicals_and_Rational_ExpressionsJust 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.
- 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_ExpressionsJust 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.
- https://math.libretexts.org/Courses/Palo_Alto_College/College_Algebra/01%3A_Prerequisites/1.04%3A_Radicals_and_Rational_ExpressionsJust 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.
- https://math.libretexts.org/Courses/Hope_College/Math_125%3A_Hope_College/01%3A_Algebra_Essentials/1.03%3A_Radicals_and_Rational_ExpressionsThe 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.
- https://math.libretexts.org/Courses/Reedley_College/College_Algebra_1e_(OpenStax)/01%3A_Algebra_Review/1.07%3A_Radicals_and_Rational_ExpressionsJust 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.
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_1350%3A_Precalculus_Part_I/01%3A_Prerequisites/1.03%3A_Radicals_and_Rational_ExpressionsJust 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.
- https://math.libretexts.org/Courses/Chabot_College/Chabot_College_College_Algebra_for_BSTEM/01%3A_Prerequisites/1.03%3A_Radicals_and_Rational_ExpressionsJust 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.
- https://math.libretexts.org/Workbench/College_Algebra_2e_(OpenStax)/01%3A_Prerequisites/1.04%3A_Radicals_and_Rational_ExpressionsJust 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.
- https://math.libretexts.org/Courses/Lumen_Learning/Beginning_Algebra_(Lumen)/08%3A_Roots_and_Rational_Exponents/8.03%3A_Operations_on_Radical_ExpressionsAs long as the roots of the radical expressions are the same, you can use the Product Raised to a Power Rule to multiply and simplify. The Product Raised to a Power Rule and the Quotient Raised to a P...As long as the roots of the radical expressions are the same, you can use the Product Raised to a Power Rule to multiply and simplify. The Product Raised to a Power Rule and the Quotient Raised to a Power Rule can be used to simplify radical expressions as long as the roots of the radicals are the same. The Product Rule states that the product of two or more numbers raised to a power is equal to the product of each number raised to the same power.
- https://math.libretexts.org/Courses/Mission_College/Math_001%3A_College_Algebra_(Kravets)/01%3A_Prerequisites/1.03%3A_Radicals_and_Rational_ExpressionsJust 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.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Developmental_Math_(NROC)/16%3A_Radical_Expressions_and_Quadratic_Equations/16.03%3A_Radical_Equations/16.3.01%3A_Solving_Radical_EquationsAn equation that contains a radical expression is called a radical equation. Solving radical equations requires applying the rules of exponents and following some basic algebraic principles. In some c...An equation that contains a radical expression is called a radical equation. Solving radical equations requires applying the rules of exponents and following some basic algebraic principles. In some cases, it also requires looking out for errors generated by raising unknown quantities to an even power.
