*But you have to be very careful there because when you square radical signs you actually lose the information that you were taking the principal square root. So the first thing I want to do is I want to isolate this on one side of the equation.Not the negative square root or not the plus or minus square root. And so when we get our final answer, we do have to check and make sure that it gels with taking the principal square root. And the best way to isolate that is to get rid of this 3.*

And this is where we actually lost some information because we would have also gotten this if we squared the negative square root of 5x plus 6. And now, this is just a straight up linear equation. So we need to make sure it actually works for the positive square root, for the principal square root. So we get 3 plus the principal square root of 5 times 15.

And so that's why we have to be careful with the answers we get and actually make sure it works when the original equation was the principal square root.

Inverse operations are critical for solving algebraic equations. The method for solving equations containing radicals involves the same process. Solve for x: The first step to solving is to remove the radical symbol by performing the inverse operation, which is to square both sides. When you square the left side, the square and square root cancel each other out, so you are left with x - 1. There is always the possibility that you will get an answer that is called an extraneous root.

For example, if you want to solve the following: x 2 = 3. To do that, you perform the inverse operation, to move the 2 to the right side of the equation. In order to isolate the x (or whatever the variable happens to be), you need to perform inverse operations to move all the numbers to the right side of the equation. That is just the most conventional way of doing things. This is an answer that seems to work, but isn't right when you check your answers.

Otherwise, I would lose the ability to say that they're equal. And now, we can square both sides of this equation.

And so the left-hand side right over here simplifies to the principal square root of 5x plus 6. So we could square the principal square root of 5x plus 6 and we can square 9. Or we get 3 plus square root of 75 plus 6 is 81 needs to be equal to 12.

And the best way to get rid of the 3 is to subtract 3 from the left-hand side.

And of course, if I do it on the left-hand side I also have to do it on the right-hand side.

We're asked to solve the equation, 3 plus the principal square root of 5x plus 6 is equal to 12.

And so the general strategy to solve this type of equation is to isolate the radical sign on one side of the equation and then you can square it to essentially get the radical sign to go away.

## Comments Solving Radical Equations Problems

## How to solve radical equations. Video Tutorial

Problem 1. Solve the radical Equation Below. Follow the steps for solving radical equations. Show Answer. Step 1. Isolate the radical. Step 1. Step 2. Square both sides. Step 2. Step 3. Solve expression. Step 3. x = 10. Step 4. Substitute answer into original radical equation to verify that the answer is…

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Free math problem solver answers your algebra homework questions with step-by-step explanations. Mathway. Visit Mathway on the web. Download free on Google Play. out of this tutoring session and select the appropriate subject from the menu located in the upper left corner of the Mathway screen.…

## Solving equations with radicals - free math help

A "radical" equation is an equation in which there is a variable inside the radical sign. Four steps to solve equations with radicals. Step 1 Isolate the radicals to left side of the equal sign. Step 2 Square each side of the equation Step 3 Solve the resulting equation Step 4 Check all solutions. Equations with one radical…

## Radical Equation Calculator - Symbolab

Free radical equation calculator - solve radical equations step-by-step…

## Radical and rational equations — Harder example

Watch Sal work through a harder Radical and rational equations problem. Watch Sal work through a harder Radical and rational equations problem. If you're seeing this message, it means we're having trouble loading external resources on our website. Problem solving…

## Solving Radical Equations - Math Is Fun

Solving Radical Equations. How to solve equations with square roots, cube roots, etc. Radical Equations A Radical Equation is an equation with a square root or cube root, etc. Solving Radical Equations. We can get rid of a square root by squaring. Or cube roots by cubing, etc…

## Braingenie Solving Word Problems Using

Engaging math & science practice! Improve your skills with free problems in 'Solving Word Problems Using Radical Equations' and thousands of other practice lessons.…

## Solving square-root equations one solution

We're asked to solve the equation, 3 plus the principal square root of 5x plus 6 is equal to 12. And so the general strategy to solve this type of equation is to isolate the radical sign on one side of the equation and then you can square it to essentially get the radical sign to go away.…

## Solving Radical Equations - ClassZone

Solving Radical Equations 437 Solve equations that contain radicals or rational exponents. Use radical equations to solve real-life problems, such as determin-ing wind speeds that corre-spond to the Beaufort wind scale in Example 6. To solve real-life problems, such as determin-ing which boats satisfy the rule for competing in the…

## Solving Radical Equations - org

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.…