lesson 3-2 ideas/vocabulary estimate square roots

Lesson 3-2 Ideas/Vocabulary

• Estimate square roots.

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Lesson 3-2 TEKS

8.1 The student understands that different forms of numbers are appropriate for different situations. (C) Approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (such as π, ).


Lesson 3-2 Example 1

Estimate Square Roots

The first perfect square greater than 54 is 64.

The first perfect square less than 54 is 49.

Estimate to the nearest whole number.

Plot each square root on a number line. Then plot .




49 < 54 < 64 Write an inequality.

72 < 54 < 82 49 = 72 and 64 = 82

Find the square root of each number.

7 < < 8 Simplify.

Answer: So, is between 7 and 8. Since 54 is closer to 49 than 64, the best whole number estimate for is 7.


A. A

B. B

C. C

D. D

Lesson 3-2 Example 1 CYP

A B

C D

0% 0%0%0%

A. 5

B. 6

C. 7

D. 8





The first perfect square greater than 41.3 is 49.

The first perfect square less than 41.3 is 36.


Plot each square root on a number line. Then plot


6 < < 7 Simplify.

Find the square root of each number.



36 < 41.3 < 49 Write an inequality.

62 < 41.3 < 72 36 = 62 and 49 = 72

Answer: So, is between 6 and 7. Since 41.3 is closer to 36 than 49, the best whole number estimate for is 6.



A. A

B. B

C. C

D. D


A B

C D

0% 0%0%0%

A. 3

B. 4

C. 5

D. 6



FINANCE If you were to invest $100 in a bank

account for two years, your investment would earn

interest daily and be worth more when you withdrew

it. If you had $120 after two years, the interest rate,

written as a decimal, would be found using the

expression . Estimate this value.

Estimate Square Roots to Solve a Problem



100 < 120 < 121 100 and 121 are the closest perfect squares.

102 < 120 < 112 100 = 102 and 121 = 112

10 < < 11 Find the square root of each number.

First estimate the value of




Answer: The approximate interest rate is 0.10 or 10%.

Since 120 is closer to 121 than 100, the best whole number estimate for is 11. Use this to evaluate the expression.




FINANCE If you were to invest $100 in a bank account

for two years, your investment would earn interest daily

and be worth more when you withdrew it. If you had $150

after two years, the interest rate, written as a decimal,

would be found using the expression .

Estimate this value.


A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D


A. 0.10

B. 0.15

C. 0.20

D. 0.25

FINANCE Estimate the value of .


lesson 3-2 ideas/vocabulary estimate square roots

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