Squares and Square Roots Math 8 11 - AGMath.com

1 Math 8 Squares and Square Square a number, multiply the number by : 2122. 3. 2)9( 4. 21110 Squares and Square Roots are Inverse x2=y then x is a Square root of positive number has two Square Roots . You will only need to indi-cate the positive Square root of a number unless this symbol appears before theradical: Practice: Solve without a 492. 3. 944. 000,810 The following Square Roots should be easy to calculate in your check by squaring your : Solve without a 100,122. 000,104. 000,640 How about 000,49?

2 Math 8 Squares and Square radical are several easy rules you must know for simplifying Square :8764496449 3109100 baba Products:991191218112181 baab Practice: Solve without a 10092. 14425 3. 4001694. 400,6255. 5032 ( think!)Math 8 Squares and Square irrational radical numbers are non-terminating, non-repeating Square Roots cannot be simplified into integers, fractions, or : 402. 753. 2518 Practice: 4902. 993. 4948 Multiplying Radical the rules we have discovered to simplify these more difficult : 15352 2.

3 5335 3. 2150356 Practice: 15235 2. 6218 3. 1851049 Math 8 Squares and Square : Simplify completely. All answers should be left in radical NOT USE A 900,43. 81364. 169165. 326. 757. 64258. 14449. 9110. 490311. 1553212. 10352 Name_____ Period _____Math 8 Squares and Square : Simplify completely. All answers should be left in radical NOT USE A 15014. 81015. 50816. 753417. 20518. 54519. 601520. 37521. 512152 22. 5189815 Math 8 You can also simplify Square Roots which include variables:For example, try the following:2xNote: This actually works only when x is positive, for example, 7)7(2 For our practice, we will assume that x represents a positive value.

4 You couldalso say that xx 2, but we will avoid this notation for :1. What about 4x?2. Now try16xbut be careful!3. How could you simplify 25x?Practice:Don t be tricked by these easy ones!Examples: 329yx5. 6241yxPractice: 6300x5. 4252xSquares and Square RootsMath 8 Squares and Square : Simplify completely. All answers should be left in radical by writing each as a product of perfect Squares where 6x2. 18a3. 12c4. 40y5. 22yx6. 1616x7. x48. 2418a9. 144c10. 25y11. 2250x12. 1040x13. 252012x14. 1012yx15.

5 9188x16. 6282ba17. 3123xx 18. 751111baab Name_____ Period _____Math 8 Rationalizing the Radicals must NOT have a radical in the the radical is called Rationalizing the : 532. 213. 11235 Practice: 1532. 833. 21124. 4523 5. yxx3258 Combining Like RadicalsExamples: 5753 2. 774 3. 15024 Practice: 226 2. 4837 3. 4520 Harder Practice: 2335 2. 722725 3. 1427712 Math 8 Radicals Quiz :100. 75 200. 30362 300. 10352 400. 21285 Addition/Subtraction (Like Terms):Simplify each:100.

6 5352 200. 188 300. 3222 400. 481275 Rationalizing the Denominator:Simplify and Rationalize each 54200. 340300. 3732 400. 143714 Math 8 Radicals Practice Period _____Simplify each: Answers should be in simplest radical form. Rationalize all WILL NOT BE ALLOWED ON THIS 1211. _____2. 500,22. _____3. 943. _____4. 444. _____5. 6a (Assume a > 0)5. _____6. 312 6. _____7. 49187. _____8. 1198. _____Math 8 Radicals Practice Period _____Simplify each: Answers should be in simplest radical form.

7 Rationalize all WILL NOT BE ALLOWED ON THIS 4925 9. _____10. 813210. _____11. 1654yx11. _____12. 68a12. _____13. 3512 13. _____14. 5072 14. _____15. 2462 15. _____Math 8 Squares and Square : Simplify completely. All answers should be left in radical NOT USE A 1212. 2255. 606. 507. 408. 279. 2514410. 62111. 225912. 183013. 221114. 55322215. 493616. 169417. 25518. 441119. 642720. 251221. 31222. 7523. 34924. 2825. 321326. 831516 Name_____ Period _____Math 8 Squares and Square : Simplify completely.

8 All answers should be left in radical NOT USE A 6x28. 7x29. 8x30. 9x31. 2xy32. 4925yx33. 34x34. 2912yx35. xx14436. 9721xx37. 222338. 351239. 245440. xx4941. 42yx42. 2549x43. 79aa44. 81a45. xx446. yxy31247. x248. 277249. 43823650. )243)(243(Name_____ Period _____Math 8 Squares and Square : Simplify completely. All answers should be left in radical NOT USE A 1442. 9005. 486. 727. 458. 329. 1004910. 181511. 24612. 171713. 204014. 75555215. 113316.

9 1694917. 64818. 63719. 252020. 184021. 8722. 31023. 31624. 23425. 44326. 731514 Name_____ Period _____Math 8 Squares and Square : Simplify completely. All answers should be left in radical NOT USE A 16x28. 25x29. 36x30. 49x31. 6ax32. 53yx33. 99x34. 222yx35. 22x36. 53515xx37. 767538. 253239. 452040. 221625xx41. 612ba42. xx92343. 1723xx44. 82x45. yx246. yx324247. 32xx48. 2535349. 1052531550. )233)(233(Name_____ Period _____Math 8 The Pythagorean TheoremThe Pythagorean Theorem:The sum of the Squares of the legs of a right triangle is equal to the Square ofits : 222cba Where a and b are the legsand c is the hypotenuse is the longest side, always opposite the right : Find the missing length : Find the missing length : Find the missing length x.

10 LEAVE ANSWERS IN RADICAL 8 The Pythagorean word problems can be solved using the Pythagorean : Solve each using the Pythagorean A rectangle has a diagonal length of 7cm and a width of its area (leave in simplified radical form).2. The wire supporting a 20-foot tall phone pole is attached to thetop of the pole, and to the ground 12 feet from the long is the wire?Practice: Solve each using the Pythagorean Find the hypotenuse of a right triangle whose legs are 7 and 24 inches What is the length of the diagonal of a Square that has 2-inch sides?