Algebra

Solution in radicals

A solution in radicals or algebraic solution is a closed-form expression, and more specifically a closed-form algebraic expression, that is the solution of a polynomial equation, and relies only on addition, subtraction, multiplication, division, raising to integer powers, and the extraction of nth roots (square roots, cube roots, and other integer roots). A well-known example is the solution of the quadratic equation There exist more complicated algebraic solutions for cubic equations and quartic equations. The Abel–Ruffini theorem, and, more generally Galois theory, state that some quintic equations, such as do not have any algebraic solution. The same is true for every higher degree. However, for any degree there are some polynomial equations that have algebraic solutions; for example, the equation can be solved as The eight other solutions are nonreal complex numbers, which are also algebraic and have the form where r is a fifth root of unity, which can be expressed with two nested square roots. See also Quintic function § Other solvable quintics for various other examples in degree 5. Évariste Galois introduced a criterion allowing one to decide which equations are solvable in radicals. See Radical extension for the precise formulation of his result. Algebraic solutions form a subset of closed-form expressions, because the latter permit transcendental functions (non-algebraic functions) such as the exponential function, the logarithmic function, and the trigonometric functions and their inverses. (Wikipedia).

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Math Tutorial for Multiplying Two Radical Expressions to the Fourth Root Together

👉 Learn how to multiply radicals. A radical is a number or an expression under the root symbol. To multiply radicals with the same root, it is usually easy to evaluate the product by multiplying the numbers or expressions inside the roots retaining the same root and then simplify the resul

From playlist How to multiply Radicals Expressions

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How to Apply the Product Rule of Radicals to Multiply an Expression

👉 Learn how to multiply radicals. A radical is an expression or a number under the root symbol. To multiply radicals with the same root, it is usually easy to evaluate the product by multiplying the numbers or expressions inside the roots retaining the same root, and then simplify the resu

From playlist How to multiply Radicals Expressions

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Learn how to simplify the product of the cube root of two numbers ex 6

👉 Learn how to multiply radicals. A radical is an expression or a number under the root symbol. To multiply radicals with the same root, it is usually easy to evaluate the product by multiplying the numbers or expressions inside the roots retaining the same root, and then simplify the resu

From playlist How to multiply Radicals Expressions

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Tutorial Simplify and Multiply the Cube Root of Two Numbers

👉 Learn how to multiply radicals. A radical is a number or an expression under the root symbol. To multiply radicals with the same root, it is usually easy to evaluate the product by multiplying the numbers or expressions inside the roots retaining the same root and then simplify the resul

From playlist How to multiply Radicals Expressions

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Multiplying the Cube root of Two Radical Expressions

👉 Learn how to multiply radicals. A radical is a number or an expression under the root symbol. To multiply radicals with the same root, it is usually easy to evaluate the product by multiplying the numbers or expressions inside the roots retaining the same root and then simplify the resul

From playlist How to multiply Radicals Expressions

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Multiplying Two Cube Root Expressions and Simplifying

👉 Learn how to multiply radicals. A radical is a number or an expression under the root symbol. To multiply radicals with the same root, it is usually easy to evaluate the product by multiplying the numbers or expressions inside the roots retaining the same root and then simplify the resul

From playlist How to multiply Radicals Expressions

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Learn How to Multiply the Cube Root of Two Radical Expressions

👉 Learn how to multiply radicals. A radical is a number or an expression under the root symbol. To multiply radicals with the same root, it is usually easy to evaluate the product by multiplying the numbers or expressions inside the roots retaining the same root and then simplify the resul

From playlist How to multiply Radicals Expressions

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Learn How to Multiply Two Radical Expressions by Simplifying Them First

👉 Learn how to multiply radicals. A radical is a number or an expression under the root symbol. To multiply radicals with the same root, it is usually easy to evaluate the product by multiplying the numbers or expressions inside the roots retaining the same root and then simplify the resul

From playlist How to multiply Radicals Expressions

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Sebastian Falkensteiner, Max Planck Institute for Mathematics in the Sciences

March 10, Sebastian Falkensteiner, Max Planck Institute for Mathematics in the Sciences Transforming radical differential equations into algebraic differential equations

From playlist Spring 2023 Online Kolchin Seminar in Differential Algebra

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Math Tutorial for Learning How to Multiply the Cube Root of Two Variable Expressions

👉 Learn how to multiply radicals. A radical is a number or an expression under the root symbol. To multiply radicals with the same root, it is usually easy to evaluate the product by multiplying the numbers or expressions inside the roots retaining the same root and then simplify the resul

From playlist How to multiply Radicals Expressions

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Solving Radical Equations

In the video, we practice solving some radical equations and list out steps we can use to solve radical equations in general. I hope this helps! Timestamps: 0:00 Introduction / 1st Example 4:15 Why do we always have to check our solutions? 6:48 Example 2 11:43 Steps for solving radical eq

From playlist College Algebra

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Nonlinear algebra, Lecture 12: "Primary Decomposition ", by Mateusz Michalek and Bernd Sturmfels

This is the twelth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.

From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra

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Let’s Solve The Radical Equation….Step-by-Step….

TabletClass Math: https://tcmathacademy.com/ Math help with solving radical equations and checking for extraneous roots or solutions. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Ma

From playlist Algebra

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Square Root(radical equation) – take your time, a lot of WORK!

How to solve a radical equation. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes. All courses d

From playlist GED Prep Videos

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Nonlinear algebra, Lecture 5: "Nullstellensätze ", by Bernd Sturmfels

This is the fifth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences. Hilbert’s Nullstellensatz is a classical result from 1890, which offers a characterization of the set of all polynomials that vanish on a given v

From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra

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The Briggs-Rausher Oscillating Reaction (Tutorial and Explanation)

This is an interesting reaction with quite drastic color changes. It is also one of the few known oscillation reactions. I followed the prepartion guide from this website: http://chemistry.about.com/cs/demonstrations/a/aa050204a.htm The information about the reaction mechanism I got from

From playlist Syntheses and Demonstrations

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No More Extraneous Roots CONFUSION – Radical Equations

TabletClass Math: https://tcmathacademy.com/ How to solve radical equations and check for extraneous roots. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algeb

From playlist GED Prep Videos

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How to Solve a Radical Equation by Rewriting Your Radical with a Rational Power

👉 Learn how to solve radical equations having one radical term. To solve a radical equation having one radical terms, we isolate the radical term by placing it in one side of the equation. Next, we get rid of the radical by taking on both sides of the equation the power corresponding to th

From playlist How to Solve Radical Equations with Higher Roots

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Radical Equations with Extraneous Solutions

In this video, we solve a few radical equations, but ones specifically that lead to extraneous solutions. We talk about how to check for extraneous solutions, what extraneous solutions are, and how we even get extraneous solutions in the first place. I pull up some graphs to help us figure

From playlist Algebra 2, Advanced Algebra, & College Algebra

Related pages

Galois theory | Radical extension | Root of unity | Quartic equation | Sextic equation | Transcendental function | Exponential function | Abel–Ruffini theorem | Division (mathematics) | Septic equation | Multiplication | Addition | Closed-form expression | Subtraction | Nth root | Algebraic expression | Nested radical | Trigonometric functions | Complex number | Cubic equation | Quadratic equation