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Solving an Equation with Radicals - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Solving equations with radicals, no matter what power, involves isolating the radical on one side of the equation and then raising both sides of the equation to the power of the radical. When solving radicals, the final step is to isolate the variable. If there are more than one radical, we isolate and remove one root, then isolate and remove the other root.finally, we solve the remaining equation for the variable.

Solving equations with a radical. So there's always a couple of steps that we have to do when we're solving equations with radicals, and those are always going to be pretty much the same thing.
First thing we want to do is isolate our radicals. So get the square roots or cube root or whatever it is by itself.
Second we need to get rid of the root and so we're going to take each side to a power. If it has a square root, we want to square both sides, if we have a cube root we want to square both sides so on and so forth. Okay? And the we just want to solve it out.
And lastly we always have to check our answers to make sure they work. So behind me I have a pretty straight forward example and we're going to solve this out, okay? So first thing we want to get our square root by itself. What we have to do is add 3 to both sides. Square root of x is equal to 5. In order to get rid of the square root we need to square. We square one side, we have to square the other to keep it balanced and so we end up with x is equal to 25, okay?
Common mistake is that when we square things people want to put plus or minus. You square something it always turns out positive okay. So it's just that one positive number giving us x25 then we need to check make sure it works. Plug in 25. Square root 25 is 5 minus 3 is 2, okay?
So by going through our steps, isolate our square root, take it to the appropriate power, solve and check. We're able to solve any equation with a radical.

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