# Radical Equations And Problem Solving

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.Yes, the picture can be extremely helpful, but it isn't proof.

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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.

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.

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. The left-hand side of the equation can be graphed as one curve, and the right-hand side of the equation can be graphed as another curve.The solution to the original equation is the intersection of the two curves. If the instructions don't tell you that you must check your answers, check them anyway.At the very least, compare your solution with a graph on your graphing calculator.If the term hasn't come up in your class yet, you should expect to hear it shortly.) By squaring both sides, I created an extra (and wrong) solution.Now I'll prove which solution is right by checking my answers.The general process for isolation is, in a sense, undoing whatever had been done to the variable in the original equation.For instance, suppose we are given the following linear equation: We can always check our solution to an equation by plugging that solution back into the original equation and making sure that it results in a true statement.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.

• ###### 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.…

Learn how to solve more challenging radical equations in this free math video tutorial by Mario's Math Tutoring. Example 1 Solving Square.…

Solving radical equations requires applying the rules of exponents and. Example. Problem. Solve. Add 3 to both sides to isolate the variable term on the left.…

• ###### Solving Radical Equations - - Algebra Help.

For a complete lesson on solving radical equations, go to 1000+ online math lessons featuring a personal math.…

• ###### Solving Radical Equations - Math is Fun

Solving Radical Equations. We can get rid of a square root by squaring. Or cube roots by cubing, etc. But Warning this can sometimes create "solutions" which.…

• ###### 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.…

• ###### 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.…