a radical equation is an equation that contains a radical

43 x

1573 x

281413 xx

A radical equationis an equation

that contains a radical.

43 x

Did you ever noticehow much sense

mathematical definitionsusually make?

The goal in solvingradical equations

is the same as the goalin solving most equations.

43 x

We need to isolatethe variable.

43 x

43 x

But there is only one wayto move the variableout from under thesquare root sign.

We need to square the

43 x

radical expression.

And, because it is anequation,

what we do to one side,

43 x

And, because it is an

24

equation,what we do to one side,

we have to do to the other.

23x

And now, we need

24

to simplify:

23x 2

3x 3x

Remember,

nn 2

no matter what n is.

(Even if n is an expression)

24 23x

3x

So we have:

16

So we have:So we have:

163x33

19x

Solve for x:

283433 xxStep 1. Simplify the expression:

Solve for x:

283433 xx

287 3x

Solve for x:

2837 xStep 1. Simplify the expression.Step 2. Isolate the radical.

Solve for x:

2837 x7 7

43 x

Solve for x:

43 xStep 1. Simplify the expression.Step 2. Isolate the radical.Step 3. Square both sides.

Solve for x:

43 x

22 43 x163 x

Solve for x:

Step 1. Simplify the expression.Step 2. Isolate the radical.Step 3. Square both sides.

163 x

Step 4. Solve the equation.

Solve for x:

163 x33

13x

Try this one:

181326 xSolve for x:

3132 x9132 x222 x11x

15555552 xxSolve for x:

15553 x

2555 x205 x4x

555 x