January 14, 2014
Tuesday, 1/14/14
Solving Radical Equations
1. Check HW/Qs?
2. Warm up
3. Notes
4. Assignment: PG 433 #'s 23, 24, 29, 36, 41, 45, 47
5. Powers Progress Check sometime this week!
Warm up
In general, you solve equations by isolating the variable; you isolate
the variable by "undoing" whatever has been done to it.
1.
2.
3.
January 14, 2014
BUT ...
Therefore,
BUT ...
Therefore,
A "radical" equation is an equation, in which at least one
variable expression is inside a radical.
For instance, this is a radical equation:
...but this is not:
January 14, 2014
To solve radical equations:
1. Isolate the radical (or one of the radicals) to one side of the
equal sign.
2. If the radical is a square root, square each side of the
equation. (If the radical is not a square root, raise each side to a
power equal to the index of the root.)
3. Solve the resulting equation.
4. Check your answer(s) to avoid extraneous roots.
Remember a square root sign in an equation means the
principal root.
1.
2.
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Remember to check for extraneous solutions.
1.
2.
5. Let's see an example where there are radicals on both sides:
January 14, 2014
6. Let's see an example where the radicals are multiplied by
constants: 7. The radical equation
graphing the system of equations
can be solved by
.
January 14, 2014