Section 7.5 Solving Square Root and Other Radical Equations

(For help, go to Lesson 5-4.) ALGEBRA 2 LESSON 7-5 Solve by factoring. 1.x 2 = –x x 2 + x = 3 3.4x 2 = –8x Check Skills You’ll Need x = –3orx = 2 x = –orx = x = orx = –

–10 + 2x + 1 = –5 Solve –10 + 2x + 1 = –5. Solving Square Root and Other Radical Equations ALGEBRA 2 LESSON 7-5 2x + 1 = 5 Isolate the radical. ( 2x + 1 ) 2 = 5 2 Square both sides. 2x + 1 = 25 2x = 24 x = 12 Check: –10 + 2x + 1 = –5 –10 + 2(12) + 1 –5 – –5 – –5 –5 = –5 7-5 Quick Check

Solving Square Root and Other Radical Equations ALGEBRA 2 LESSON 7-5 Solve 3(x + 1) = x + 1 = 32Simplify. x = 31 3(x + 1) = (x + 1) = 8Divide each side by Check: 3(x + 1) = 24 3(31 + 1) 24 3(2 5 ) 24 3(2) = ((x + 1) ) = 8 Raise both sides to the power (x + 1) 1 = 8 Multiply the exponents and Quick Check

Solving Square Root and Other Radical Equations ALGEBRA 2 LESSON 7-5 An artist wants to make a plastic sphere for a sculpture. The plastic weighs 0.8 ounce per cubic inch. The maximum weight of the sphere is to be 80 pounds. The formula for the volume V of a sphere is V = r 3, where r is the radius of the sphere. What is the maximum radius the sphere can have? Define: Let r = radius in inches. Relate: volume of sphere density of plastic maximum weight Write: r < – < – 7-5

Solving Square Root and Other Radical Equations ALGEBRA 2 LESSON 7-5 (continued) The maximum radius is about 2.88 inches. 4 r r 3r < – r 3r 3 75 < – Use a calculator.r 2.88 < – < – 7-5 Quick Check

Solving Square Root and Other Radical Equations ALGEBRA 2 LESSON 7-5 Solve x + 2 – 3 = 2x. Check for extraneous solutions. x + 2 – 3 = 2x x + 2 = 2x + 3Isolate the radical. ( x + 2) 2 = (2x + 3) 2 Square both sides.0 = 4x x + 7Combine like terms. 0 = (x + 1)(4x + 7)Factor. x + 2 = 4x x + 9Simplify. x + 1 = 0 or 4x + 7 = 0Factor Theorem x = –1 orx = –

Check: x + 2 – 3 = 2x x + 2 – 3 = 2x –1 + 2 – 3 2(–1) + 2 – – 3 –2 – 3 –2 = –2 – – 7474 – – 7272 – = – 5252 / 7474 – Solving Square Root and Other Radical Equations ALGEBRA 2 LESSON 7-5 (continued) The only solution is – Quick Check

Solving Square Root and Other Radical Equations ALGEBRA 2 LESSON 7-5 Solve (x + 1) – (9x + 1) = 0. Check for extraneous solutions x = 0 or x = 7 (x + 1) 2 = 9x + 1 x 2 + 2x + 1 = 9x + 1 x 2 – 7x = 0 x(x – 7) = 0 (x + 1) – (9x + 1) = (x + 1) = (9x + 1) ((x + 1) ) 3 = ((9x + 1) )

Solving Square Root and Other Radical Equations ALGEBRA 2 LESSON 7-5 (continued) Check: (x + 1) – (9x + 1) =0 (x + 1) – (9x + 1) = 0 (0 + 1) – (9(0) + 1) 0(7 + 1) – (9(7) + 1) 0 (1) – (1) 0 (8) – (64 ) 0 (1) – (1 2 ) 0 (8) – (8 2 ) 0 1 – 1 = 0 8 – 8 = Both 0 and 7 are solutions. 7-5 Quick Check

Solving Square Root and Other Radical Equations ALGEBRA 2 LESSON 7-5 Solve each equation. Check for extraneous solutions x – 1 = (x – 9) = x – 1 = x – 8 4.(4x + 3) = (16x + 44) 5.A circular table is to be made that will have a top covered with material that costs $3.50 per square foot. The covering is to cost no more than $60. What is the maximum radius for the top of the table? –, 5454 about 2.34 ft 7-5