Easy Guide to Radicals

1. Easy Guide to Radicals Miss Gould October 17, 2011

2. Simplifying Square Roots • Do you know the perfect squares? • A square is a number which is the result of 2 identical numbers being multiplied together • Ex. 4 X 4 = 16 • 16 is a perfect square

3. Perfect Squares • You should memorize these perfect squares: • 1² = 1 11² = 121 • 2² = 4 12² = 144 • 3² = 9 13² = 169 • 4² = 16 14² = 196 • 5² = 25 15² = 225 • 6² = 36 16² = 256 • 7² = 49 17² =289 • 8² = 64 18² =324 • 9² = 81 19² = 361 • 10² = 100 20²= 400

4. Simplifying Radicals • How do you simplify

5. 1. Check to see if the radicand is already a perfect square. If so, write the square root. • 2. Push Y= on your calculator and then 2nd Graph • 3. Next to Y1 = type in 98, then divide, then X (next to the green ALPHA key) • 4. You should get a table with X in one column and Y1 in the other.

6. 5. Be sure it says X=1 under the table. • 6. Use the arrow keys to scroll until you find the largest perfect square. • For 98 the largest perfect square is 2 X 49 (49 is a perfect square)

8. Next….. • The square root of 49 is 7 • Put the 7 on the outside • And the 2 ( remember it was 49 X 2) on the inside

9. =

10. How do you simplify…..

11. The radicand is a perfect square • 1. Check to see if the radicand (36) is already a perfect square. • 2. Find the square of 36 = 6 • 6 X 6 = 36 • Use the other 6 to multiply it with the 2 • 2 X 6 = 12 • 3. Your answer is • 2. Push Y= on your calculator and then 2nd Graph • 3. Next to Y1 = type in 98, then divide, then X (next to the green ALPHA key) • 4. You should get a table with X in one column and Y1 in the other.

12. Radicand NOT a perfect square 96 Is not a perfect square Push Y= on your calculator and then 2nd Graph Next to Y1 = type in 96, then divide, then X (next to the green ALPHA key) You should get a table with X in one column and Y1 in the other.

13. Next….. Be sure it says X=1 under the table. Use the arrow keys to scroll until you find the largest perfect square. 16 is the largest perfect square

14. Not a perfect square Find the square root of 16 4 x 4 = 16 Take one of the 4s and multiply it with the 10 4 x 10 = 40 You still have the 6 left (from 16 x 6) Your answer is

15. Try another….. • Not a perfect square: • Is 45 a perfect square? No • 2. Enter Y= 45/x second graph • to get the table of factors • 49 is the largest square • 5 X 49 = 245 • 3. • The square root of 49 is 7 (7 x 7 = 49) • Multiply the outside number by 7 to get 63 • . Bring down the 5 (from 5 x 49) • Answer:

16. And another • Is 200 a perfect square? • Click Y= and type in 200/X • Second graph to get the table • 100 is the largest square • 100 X 2 • The square root of 100 s 10. • 10 X 2 = 100, leaving you a 2 • Your answer is:

17. Practice Time 1. Is 75 a perfect square? No Type 75 into the factors chart in your calculator 25 is the larges square because 25 x 3 = 25 The square root of 25 is 5. Your answer is

18. Practice Time Is 405 a perfect square? NO Y= 405/x The largest square factor is 81 because 5 x 81 = 405 The square root of 81 is 9. Multiply 9 X 3 (the outside number) to get 27 You are left with 5 Your answer is

19. Find the square root of fractions! • Is 49 a perfect square? YES • Is 196 a perfect square? YES 3. Find the squares of both! 4. Your answer: or

20. Find the square root of negative integers -- Is 1 a perfect square? YES ( 1 x 1 = 1) Is 4 a perfect square? YES (2 x 2 = 4) Your answer is ---

21. Multiplying Radicals = X Must reduce if possible Example: = 6 =