Solving equations which
contain radicals involves using the *squaring
property of equality*. This property allows us to raise each side
of an equation which contains a radical term by a power equal to the power
of the index of the radical. This will eliminate the radical and then
we can solve the resulting equation using a method which we have learned
earlier … isolation if the equation is a first-degree equation and factoring
if the equation is a quadratic (second-degree) equation. Note: *All potential
solutions from the squared equation must be checked in the original
equation, *since squaring could provide us with an *extraneous* solution.

To solve these equations involving square roots:

1) isolate the
radical,

2) square both sides,

3) combine like terms,

4) determine whether the
resulting equation is a first-degree
(if so, use isolation to solve) or a second-

degree (if so, use factoring
to solve) and

5) check the solution for validity.

Example 1 involves a first-degree equation and Example 2
involves a second-degree equation.

Example 1. Solve:

Check:
is true and therefore a valid answer.

Example 2. Solve:

Therefore,
and

Check:
is not true and therefore
is an invalid answer.

is true and therefore
is a valid answer.