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Section 9.1
Solving Quadratic Equations by the Square Root Property
Observe:
If
, then
___________________.
Square Root Property of Equations
If is a positive number and if
then
Example 1
Solve each equation by using the square root property. Simplify all radicals.
a)
b)
c)
How to Solve an Equation by the Square Root Property
1. __________________ the squared term.
2. Take ____________________________ of both sides, remembering the _________.
3. Solve for the variable.
Example 2
Solve each equation by using the square root property. Simplify all radicals.
a)
b)
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To solve an equation of the form: (
Apply the Square Root Property, using
)
√
as the base:
Example 3
Solve each equation by using the square root property. Simplify all radicals.
a)
(
)
b)
(
c)
(
)
d)
(
)
)
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Now let’s try a few application problems…
Example 4
The formula
is used to approximate the weight of a bass, in pounds, given its length and its girth ,
both measured in inches. Approximate the length of a bass weighing 2.80 lb and having girth
11 in.
Example 5
The area of a circle with radius is given by the formula
If a circle has area
, what is its radius?