Calculating Square Roots – Part 1

1. Calculating Square Roots – Part 1 Slideshow 3, Mr Richard Sasaki, Room 307

2. Objectives • Recall how to calculate simple square roots • Calculate square roots to one decimal place or two significant figures • Understand cubed roots and other roots

3. Square Roots Square roots use the symbol where the number on the right is rooted. So for we’d say “the square root of 4” or just “root 4”. Mathematics is international but there is some disagreement about roots. What is ?

4. One or Two Solutions . You need to be understanding that for me (I’m Welsh), = However, in some countries, (at least in America), = 3. This will complicate our problems but it’s a very good idea to understand both. Wales America = = = (All the same.)

5. One or Two Solutions In a general case please assume that . If something says “find the positive solution” then of course let . In geometry, makes no sense so almost always . Let’s try some questions! So, what do we do?

6. Answers We could get +, + or +, - or -, + or -, -. As two negative numbers squared make a positive and two positive numbers make a positive, we can’t square root a negative. (one solution as it was squared).

7. Trial and Error We can use a process called Trial and Error. We make a guess and check to see if it is too high or low, then we continue until we get as close to the number as we need to. How can we estimate ? What number do we square to make 2? (Too low) (Too high) (Too high) (Too low) The square root of 2 (to one decimal place) is between 1.4 and 1.5 but closer to 1.4.

8. Trial and Error What number do we square to make 34? Let’s try to 2 significant figures. (Too low) (Too high) It’s close to 6… (Too low) (Too low) (Too high) The square root of 34 (to 2 significant figures) is between 5.8 and 5.9 but closer to 5.8.

9. Answers

10. Other Roots We know square rooting can produce up to two solutions, how about cube rooting? (as ) We can cube root a negative number but not square root it. (Square rooting it would produce an imaginary number.) How about the fourth root? (as )

11. So… For … And so on! Example Calculate and . (as but ) (as and )

12. Answers