Real Numbers And The Pythagorean Theorem Worksheet - Chapter 7 Page 6
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46Squaring a positive number and fi nding a square root are inverse operations.
You can use this relationship to evaluate expressions and solve equations
involving squares.
Evaluating Expressions Involving Square Roots
3 3
EXAMPLE
Evaluate each expression.
—
√
36 + 7 = 5(6) + 7
a. 5
Evaluate the square root.
= 30 + 7
Multiply.
= 37
Add.
—
√
—
1
18
1
√
+
=
+
—
—
—
b.
9
Simplify.
4
2
4
1
=
+ 3
—
Evaluate the square root.
4
1
= 3
—
Add.
4
—
(
)
2
√
− 5 = 81 − 5
c.
81
Evaluate the power using inverse operations.
= 76
Subtract.
4 4
Real-Life Application
EXAMPLE
The area of a crop circle is 45,216 square feet. What is the radius
of the crop circle? Use 3.14 for �� .
A = π r
2
Write the formula for the area of a circle.
≈ 3.14
2
Substitute 45,216 for A and 3.14 for π .
45,216
3.14r
14,400 = r
2
Divide each side by 3.14.
—
—
√
√
14,400 =
2
r
Take positive square root of each side.
120 = r
Simplify.
The radius of the crop circle is about 120 feet.
Evaluate the expression.
√
—
Exercises 20–27
—
—
28
(
)
2
√
√
7. 12 − 3
+ 2.4
9. 15 −
—
25
8.
4
7
10. The area of a circle is 2826 square feet. Write and solve an
equation to fi nd the radius of the circle. Use 3.14 for π .
Section 7.1
Finding Square Roots
291
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