Solving Radical Equations

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Presentation transcript:

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

BACK

BACK

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