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3-9

Finding Square Roots

Warm Up

Problem of the Day

Lesson Presentation

Course 3

Warm Up Find the two square roots of each

number. Evaluate each expression.

12

16

20

119

Problem of the Day A pyramid of blocks is built

in layers. The bottom layer has 62, or 36,

blocks. The next layer has 52 blocks, and so on

until the top layer has 1 block. How many

blocks are there in all?

91 blocks

3-9

Finding Square Roots

Learn to estimate square roots to a given number

of decimal places and solve problems using square

roots.

Course 3

A museum director wants to install a skylight to

illuminate an unusual piece of art. It must be

square and have an area of 300 square inches,

with wood trim around it. Can you calculate the

trim that you need? You can do this by using your

knowledge of squares and square roots.

Additional Example 1A Estimating Square Roots of

Numbers

Each square root is between two integers. Name

the integers.

Think What are perfect squares close to 55?

55

A.

49 lt 55

72 49

64 gt 55

82 64

Additional Example 1B Estimating Square Roots

of Numbers Continued

Each square root is between two integers. Name

the integers.

Think What are perfect squares close to 90?

90

B.

81 lt 90

92 81

100 gt 90

102 100

Try This Example 1A

Each square root is between two integers. Name

the integers.

Think What are perfect squares close to 80?

80

A.

64 lt 80

82 64

81 gt 80

92 81

Try This Example 1B

Each square root is between two integers. Name

the integers.

Think What are perfect squares close to 45?

45

B.

36 lt 45

62 36

49 gt 45

72 49

Additional Example 2 Problem Solving Application

You want to sew a fringe on a square tablecloth

with an area of 500 square inches. Calculate the

length of each side of the tablecloth and the

length of fringe you will need to the nearest

tenth of an inch.

First find the length of a side. Then you can use

the length of a side to find the perimeter, the

length of fringe around the tablecloth.

Additional Example 2 Continued

Additional Example 2 Continued

Because 500 is between 222 and 232, the square

root of 500 is between 22 and 23.

The square root is between 22.3 and 22.4.

Additional Example 2 Continued

The square root is between 22.3 and 22.4. To

round to the nearest tenth, look at the next

decimal place.

Consider 22.35.

Too low

22.352 499.5225

The square root must be greater than 22.35, so

round up.

The length of each side of the table is about

22.4 in.

Additional Example 2 Continued

Solve

The length of a side of the tablecloth is 22.4

inches, to the nearest tenth of an inch. Now

estimate the length around the tablecloth.

4 22.4 89.6

Perimeter 4 side

You will need about 89.6 inches of fringe.

Additional Example 2 Continued

The length 90 inches divided by 4 is 22.5 inches.

A 22.5-inch square has an area of 506.25 square

inches, which is close to 500, so the answers are

reasonable.

Try This Example 2

You want to build a fence around a square garden

that is 250 square feet. Calculate the length of

one side of the garden and the total length of

the fence, to the nearest tenth.

First find the length of a side. Then you can use

the length of a side to find the perimeter, the

length of the fence.

Try This Example 2 Continued

Try This Example 2 Continued

Because 250 is between 152 and 162, the square

root of 250 is between 15 and 16.

1

2

3

4

The square root is between 15.8 and 15.9.

Try This Example 2 Continued

To round to the nearest tenth, look at the next

decimal place.

15.852 251.2225

Consider 15.85.

The square root is lower than 15.85, so round

down.

The length of each side of the garden is about

15.8 ft.

Try This Example 2 Continued

Solve

The length of a side of the garden is 15.8 feet,

to the nearest tenth of a foot. Now estimate the

length around the garden.

4 15.8 63.2

Perimeter 4 side

You will need about 63.2 feet of fence.

Try This Example 2 Continued

The length 63.2 feet divided by 4 is 15.8 feet. A

15.8 foot square has an area of 249.64 square

feet, which is close to 250, so the answers are

reasonable.

Additional Examples 3 Using a Calculator to

Estimate the Value of a Square Root

Use a calculator to find 500. Round to the

nearest tenth.

Using a calculator, 500 22.36067977.

Rounded, 500 is 22.4.

Try This Example 3

Use a calculator to find 200. Round to the

nearest tenth.

Rounded, 200 is 14.1.

Lesson Quiz

Each square root is between two integers. Name

the two integers.

1. 27 2. 456

5 and 6

22 and 21

Use a calculator to find each value. Round to the

nearest tenth.

9.4

35.0

3. 89 4. 1223

5. A square field has an area of 2000 square

feet. To the nearest foot, how much fencing would

be needed to enclose the field?

179 ft

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