a radical equation is an equation that contains a radical
TRANSCRIPT
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