When you do this-- when you square this, you get 5x plus 6. So we get x is equal to 15, but we need to make sure that this actually works for our original equation. And this is the principal root of 81 so it's positive 9.

If you square the square root of 5x plus 6, you're going to get 5x plus 6. On the left-hand side, we have 5x and on the right-hand side, we have 75. We get x is equal to-- let's see, it's 15, right? Maybe this would have worked if this was the negative square root. So it's 3 plus 9 needs to be equal to 12, which is absolutely true.

Substitute 17 in for x, and we get √(17 - 1) = 4, or √(16) = 4.

For this problem, the number 17 works, so we have confirmed it as the answer.

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.If there is only one radical in an equation, it can be solved by isolating the radical and raising both sides to the power necessary to eliminate the radical.Please keep in mind that in solving radical equations, sometimes there are extraneous solutions. As a member, you'll also get unlimited access to over 79,000 lessons in math, English, science, history, and more.Plus, get practice tests, quizzes, and personalized coaching to help you succeed.That means, you subtract (the opposite of add) 2 from both sides of the equation. This is why, with problems containing radicals, you always have to check your answer.It is not common, but there can be an answer that doesn't work.This lesson will give you some of the knowledge that you need to become an algebra master. You might be thinking (and rightly so) that a radical is someone who speaks out against injustices.They want to do things in a new and unconventional way.If you're seeing this message, it means we're having trouble loading external resources on our website.If you're behind a web filter, please make sure that the domains *.and *.are unblocked.

## Comments Solving Radical Equations Problems

## 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 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.…

## 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…

## 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…

## Radical Equation Calculator - Symbolab

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

## Mathway Algebra Problem Solver

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.…

## 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 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.…