Solving Radical Equations
that contains a radical. A radical equation is an equation that contains a radical. BACK
in solving most equations. The goal in solving radical equations is the same as the goal in solving most equations. BACK
We need to isolate the variable. BACK
But there is only one way to move the variable out from under the square root sign. BACK
We need to square the radical expression. BACK
And, because it is an equation, what we do to one side, BACK
we have to do to the other. And, because it is an equation, what we do to one side, we have to do to the other. BACK
(Even if n is an expression) Remember, no matter what n is. (Even if n is an expression) BACK
So we have: BACK
Solve for x: Step 1. Simplify the expression: BACK
Solve for x: BACK
Solve for x: Step 1. Simplify the expression. Step 2. Isolate the radical. BACK
Solve for x: BACK
Solve for x: Step 1. Simplify the expression. Step 2. Isolate the radical. Step 3. Square both sides. BACK
Solve for x: BACK
Solve for x: Step 1. Simplify the expression. Step 2. Isolate the radical. Step 3. Square both sides. Step 4. Solve the equation. BACK
Solve for x: BACK
Try this one: Dude! You try one. BACK
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Try this one: Dude! You try one. BACK
No Solutions If you have a square root equaling a negative number there is no solution.
An Extraneous Solution is a solution that does not satisfy the original equation. -2 is an extraneous answer.
Watch Out!! If all answers are extraneous, there is also no solution.
Since -11 does not satisfy the original equation, 11 is the only solution. -11 is an extraneous solution.
Solving Radical Equations BACK