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.