Algebra I Concept Test # 12 – Square Roots 1. Expand: 5.361 x 10−2 Note: To expand shift decimal point 0.05361 2. Simplify: 4(m3 n −2) −5 • (− 3mn4)2 4m−15 n10 • (−3)2m2n8 4m−15n10 • 9m2n8 Power to a Power  Multiply exponents Simplify 36m−15 n10 • m2n8 Multiply Product of Powers Property 36m−13 n18 Negative Exponent Property 36n18 m13 © 2007-09 by S-Squared, Inc. All Rights Reserved.

Algebra I Concept Test # 12 – Square Roots Simplify: 3. (− 2r2t3)3 (− 2)3r6t9 8r−3t 9 8r−3t 9 Power to a Power  Multiply exponents − 8r6t9 − 1r6t9 Simplify 8r−3t 9 r−3t 9 − r6 – (−3)t9 – 9 − r9t0 Quotient of Powers Subtract exponents − r9 • 1 Zero Exponent property − r9

Algebra I Concept Test # 12 – Square Roots 4. The Euler Company has fixed costs of $800 per week. Each item produced by the company costs $3 to manufacture and can be sold for $7. a) How many items must be produced to reach the break-even point (Income = Cost)? Let, a = dollar amount i = number of items Write two Equations: 3i + 800 = a 7i = a Substitution: 3i + 800 = 7i Subtract 3i: 800 = 4i Divide by 4: 200 = i 200 items

Algebra I Concept Test # 12 – Square Roots 4. The Euler Company has fixed costs of $800 per week. Each item produced by the company costs $3 to manufacture and can be sold for $7. b) How much does the company have to make to break-even? Let, a = dollar amount i = number of items Equations: 3i + 800 = a i = 200 items Substitution: 3(200) + 800 = a Simplify: 600 + 800 = a Divide by 4: 1400 = a $ 1400.00

Algebra I Concept Test # 12 – Square Roots Simplify: 5. 5 • 15 5 • 15 75 25 • 3 25 • 3 Product Property of Radicals 5 3 6. 81x10 81 • x10 Product Property of Radicals 9x5

Algebra I Concept Test # 12 – Square Roots Simplify: 1 1 7. 64 • 8 Simplify 2 2 4 8. 18 9 9 Reduce 32 16 16 Quotient Property of Radicals 3 Simplify 4

Algebra I Concept Test # 12 – Square Roots Simplify: 9. 6x2y10 6 • x2 • y10 Product Property of Radicals x y5 6

Algebra I Concept Test # 12 – Square Roots Simplify: 10. 2 7 ─ 3 28 Rewrite Radicand with perfect square factor Term is in simplest form, Radicand is prime 2 7 ─ 3 4 • 7 2 7 ─ 3 • 2 7 Square Root 2 7 ─ 6 7 Multiply − 4 7 Subtract

Algebra I Concept Test # 12 – Square Roots 11. Approximate the following square roots to the tenths place: a) 10 Approximately 3.2 **Notice the square root of 9 is 3 and the square root of 16 is 4. Since 10 is between 9 and 16, the square root of 10 must be between 3 and 4. b) 79 Approximately 8.9 **Notice the square root of 64 is 8 and the square root of 81 is 9. Since 79 is between 64 and 81, the square root of 79 must be between 8 and 9.

Algebra I Concept Test # 12 – Square Roots 12. Evaluate: a + bc for a = 8, b = − 4, and c = − 9 2 Substitute (8)2 + (−4)(−9) 64 + (−4)(−9) Exponent 64 + 36 Multiply 100 Add 10 Square Root

Algebra I Concept Test # 12 – Square Roots 13. Distribute ( 3 ─ 8) 5 15 ─ 8 5 Simplify: 14. 8a3b • 8a−1b3 64a2b4 Multiply 64 • a2 • b4 Product Property of radicals 8ab2 Square Root

Algebra I Concept Test # 12 – Square Roots Solve: 15. 7 + 3 x = 22 Isolate the radical x – 7 – 7 Subtract 3 x = 15 Divide 3 3 ( )2 ( )2 x = 5 Square x = 25

Algebra I Concept Test # 12 – Square Roots Solve: Combine like terms 16. 2 x + 4 x = 42 6 x = 42 Divide 6 6 ( )2 ( )2 x = 7 Square x = 49 17. Check your solution for #16. 2 x + 4 x = 42 2 49 + 4 49 = 42 Substitute 2 • 7 + 4 • 7 = 42 Simplify 14 + 28 = 42 42 = 42 Check Complete

Algebra I Concept Test # 12 – Square Roots Solve: 18. 5 x ─ 11 x ─ 10 = 14 Isolate the radical x − 6 x ─ 10 = 14 Combine like terms + 10 + 10 Add − 6 x = 24 Divide − 6 − 6 x = − 4 Note: The square root of a number can never be negative No Solution

Algebra I Concept Test # 12 – Square Roots 19. Using the square root function, y = x – 7, complete the following: y = x – 7 a) Complete the table b) Graph the function using the ordered pairs from part a. Note: Substitute each of the given x-coordinates into the given radical equation to find the y-coordinate. x y 4 − 5 1 2 3 − 1 − 5 − 4 − 3 − 2 x y 5 4 − 7 − 6 1 − 6 1/4 − 6 1/2 − 7

Algebra I Concept Test # 12 – Square Roots 19. Using the square root function, y = x – 7, complete the following: RADICAL c) Identify the endpoint (0, − 7) d) Identify the y-intercept (0, − 7) e) Identify the x-intercept (49, 0) f) State the domain x ≥ 0 x y g) State the range y ≥ − 7 4 − 5 1 2 3 − 1 − 5 − 4 − 3 − 2 x y 5 4 − 7 − 6 Note: Let y = 0 and then solve for x. 1 − 6 1/4 − 6 1/2 0 = x – 7 − 7 7 = x 49 = x