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Bell Ringer

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**Simplifying Square Roots**

An expression written with a radical symbol is called a radical expression, or a radical. The number or expression inside the radical is the radicand.

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**Calculator keystrokes**

Example 1 Use a Calculator to Find Square Roots Find the square root of 52. Round your answer to the nearest tenth. Check that your answer is reasonable. SOLUTION Calculator keystrokes or Display Rounded value ≈ 7.2 52 This is reasonable, because 52 is between the perfect squares 49 and 64. So, should be between and , or 7 and 8. The answer 7.2 is between 7 and 8. 52 64 49 3

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Example 2 Find Side Lengths Use the Pythagorean Theorem to find the length of the hypotenuse to the nearest tenth. SOLUTION a2 + b2 = c2 Write Pythagorean Theorem. = c2 2 3 Substitute for a and for b. 2 + 3 = c2 Simplify. 5 = c2 Add. Take the square root of each side. = c 5 Use a calculator. 2.2 ≈ c 4

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**Multiply the radicals. Then simplify if possible.**

Example 3 Multiply Radicals Multiply the radicals. Then simplify if possible. b. 2 8 a. 3 7 SOLUTION a. 3 7 = b. = 2 8 = 21 = 16 = 4 5

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**Simplify the radical expression.**

Example 4 Simplify Radicals Simplify the radical expression. a. 12 b. 45 SOLUTION = a. 12 4 3 b. 45 9 5 = = 4 3 = 9 5 = 2 3 = 3 5 6

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Now You Try Evaluate, Multiply, and Simplify Radicals Find the square root. Round your answer to the nearest tenth. Check that your answer is reasonable. 1. 27 ANSWER 5.2; < < , so 5 < 5.2 < 6. 25 27 36 2. 46 ANSWER 6.8; < < , so 6 < 6.8 < 7. 46 36 49 3. 8 ANSWER 2.8; < < , so 2 < 2.8 < 3. 4 8 9 4. 97 ANSWER 9.8; < < , so 9 < 9.8 < 10. 97 81 100

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**Multiply the radicals. Then simplify if possible.**

Checkpoint Now You Try Evaluate, Multiply, and Simplify Radicals Multiply the radicals. Then simplify if possible. 5. 3 5 ANSWER 15 6. 11 6 ANSWER 66 7. 27 3 ANSWER 9 8. 5 3 15 ANSWER

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**Simplify the radical expression.**

Checkpoint Now You Try Evaluate, Multiply, and Simplify Radicals Simplify the radical expression. 9. 20 ANSWER 2 5 10. 8 ANSWER 2 11. 75 ANSWER 5 3 12. 112 ANSWER 4 7

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