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Lesson Menu Five-Minute Check (over Chapter 9) Then/Now New Vocabulary Key Concept: Square Root Example 1: Find Square Roots Example 2: Estimate Square Roots Example 3: Use a Calculator to Estimate a Square Root Example 4: Use a Calculator to Estimate a NegativeExample 4: Use a Calculator to Estimate a Negative Square RootSquare Root Example 5: Real World Example: Use Square Roots to Solve Problems

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Over Chapter 9 5-Minute Check 1 A.10a 2 b 3 B.5 2 a 2 b 3 C.10ab 5 D.5ab 5 Write 5 5 a a b b b using exponents.

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Over Chapter 9 5-Minute Check 2 A.2xy B. 4xy C. 4(xy) 4 D.(xy) 4 Write x y x y x y x y using exponents.

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Over Chapter 9 5-Minute Check 3 A.3 20 B.3 10 C.3 9 D.9 20 Find 3 5 3 4. Express using positive exponents.

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Over Chapter 9 5-Minute Check 4 A.–35a 5 B.–12a 6 C.–12a 5 D.35a 5 Find (5a 2 ) (–7a 3 ). Express using positive exponents.

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Over Chapter 9 5-Minute Check 5 A. B. C. D. Express using positive exponents

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Over Chapter 9 5-Minute Check 6 A.y = 3x 3 B.y = 3x 2 + 2x – 2 C.y = 3x – 2 D.y = 3x Which of the following equations represents the graph shown?

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Then/Now You have already evaluated expressions containing squares of numbers. (Lesson 8–1) Find square roots. Estimate square roots.

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Vocabulary perfect square square root radical sign

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Concept

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Example 1 A Find Square Roots Answer: 8 A.

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Example 1 B Find Square Roots Answer: –11 B.

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Example 1 C Find Square Roots Answer: +16 and –16

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Example 1 D Find Square Roots Answer: There is no square root because no number times itself is equal to –9. D.

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Example 1 CYP A A.624 B.12.5 C.5 D.–5 A.

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Example 1 CYP B A.12 B.–12 C.–72 D.–20,736 B.

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Example 1 CYP C A.4 B.–4 C.4 and –4 D.256 and –256 C.

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Example 1 CYP D A.–8 B.8 C.–32 D.There is no real square root. D.

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Example 2 A Estimate Square Roots Answer: 5 A. The first perfect square less than 22 is 16. The first perfect square greater than 22 is 25.

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B. Example 2 B Estimate Square Roots Answer: –18 The first perfect square less than 319 is 289. The first perfect square greater than 319 is 324.

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Example 2 CYP A A.6 B.7 C.8 D.9 A.

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Example 2 CYP B A.–6 B.–7 C.6 D.7 B.

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Example 3 Use a Calculator to Estimate a Square Root Use a calculator. Round to the nearest tenth. Check for Reasonableness Since 8 2 = 64, the answer is reasonable. ENTER2nd 577.549834435

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Example 3 A.3.9 B.9.8 C.38.5 D.There is no real square root.

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Example 4 Use a Calculator to Estimate a Negative Square Root Use a calculator. Round to the nearest tenth. Check for Reasonableness Since 7 2 = 49, the answer is reasonable. ENTER2nd 426.480740698

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Example 4 A.–8.5 B.–36.0 C.8.5 D.There is no real square root.

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Example 5 Use Square Roots to Solve Problems SKYSCRAPER The tallest building in Houston, Texas, is the JP Morgan Chase Tower, standing at 1002 feet. About how far to the horizon can a person standing on the top floor see? Round your answer to the nearest tenth. Replace h with 1002. Evaluate the square root first. Write the formula.

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Example 5 Use Square Roots to Solve Problems 38.6Multiply. Answer: On a clear day, a person could see about 38.6 miles.

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Example 5 A.23.2 miles B.23.3 miles C.23.7 miles D.24.4 miles

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End of the Lesson

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What does it mean when we see numbers written like this: 4²10² 9² Since our exponent is 2, it means that we multiply the number by itself! So we have.

What does it mean when we see numbers written like this: 4²10² 9² Since our exponent is 2, it means that we multiply the number by itself! So we have.

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