Chapter Thirteen — Radical Expressions and Equations
The Humongous Book of Algebra Problems
288
Solving Radical Equations
Use exponents to cancel out radicals
13.32 Solve the equation for x.
To solve for x, you must eliminate the square root from the equation. To
eliminate a root with index 2, raise both sides of the equation to the second
power.
Squaring a square root, cubing a cube root, or more generally raising an nth
root to the n power will eliminate the radical symbol, leaving only the radicand.
Solve for x by subtracting 2 from both sides of the equation.
13.33 Solve the equation for x.
Isolate the radical expression by adding 1 to both sides of the equation.
Eliminate the square root by squaring both sides of the equation.
13.34 Solve the equation for x and verify your answer.
Isolate the radical expression left of the equal sign.
Don’t square
both sides of the
equation to get rid
of the square root
until you’ve got the
radical all by itself
on one side of the
equal sign.
Chapter Thirteen — Radical Expressions and Equations
The Humongous Book of Algebra Problems
289
Eliminate the radical expression and solve for x.
To verify the answer, substitute x = –4 into the original equation. The result
should be a true statement.
13.35 Solve the equation for x.
Isolate the radical expression left of the equal sign.
Eliminate the square root by squaring both sides of the equation.
13.36 Solve the equation for x: .
Add to both sides of the equation to separate the radical expressions.
Eliminate the square roots by squaring both sides of the equation.
The index of
the radical is 3,
so raise both sides
to the third power.
Don’t forget to cube
the number on the
right side of the
equation.
If you squared
both sides without moving one
of the radicals, you’d get
,
which is not nearly as easy
to deal with.
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