# Radical Equations And Problem Solving

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.

For most of this lesson, we'll be working with square roots.

For instance, this is a radical equation, because the variable is inside the square root: In general, we solve equations by isolating the variable; that is, we manipulate the equation to end up with the variable on one side of the "equals" sign, with a numerical value on the other side.

On the left-hand side of this equation, I have a square root. On the right-hand side, I've got a positive number.

Since both sides are known positive, squaring won't introduce extraneous solutions.

But I'll check my solution at the end, anyway, because the instructions require it.

First, I'll square both Because of this fact, my squaring of both sides of the equation will be an irreversible step.

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.

For instance, in my first example above, " Squaring both sides of an equation is an "irreversible" step, in the sense that, having taken the step, we can't necessarily go back to what we'd started with.

By squaring, we may have lost some of the original information.

• ###### Solving Radical Equations - CliffsNotes

A radical equation is an equation in which a variable is under a radical. If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting. Since radicals with odd indexes can have negative answers, this problem does.…

• ###### Solving square-root equations one solution video Khan.

Take for example the problem in this video. If he had not. In general, when we solve radical equations, we often look for real solutions to the equations. So yes.…

• ###### Solving Radical Equations - ChiliMath

Learning how to solve radical equations requires a lot of practice and familiarity of the different types of problems. In this lesson, the goal is to show you detailed.…

• ###### Radical Expressions and Equations -

Algebra 1 answers to Chapter 10 - Radical Expressions and Equations - Chapter Review - 10-4 Solving Radical Equations - Page 643 45 including work step by step written by community members like you.…

• ###### Solving Radical Equations - GitHub Pages

Radical Equations. A radical equation Any equation that contains one or more radicals with a variable in the radicand. is any equation that contains one or more radicals with a variable in the radicand. Following are some examples of radical equations, all of which will be solved in this section…

• ###### Squares and Square Roots Solving Radical Equations

A radical equation is an equation that features a variable contained inside a radicand. At least it won't get wet if it rains. An example of a radical equation is. The equation is not a radical equation, because the variable doesn't occur inside the radicand. The 5 and 9 are making it wait outside.…