Hello! I am a student of homeschooling, grade 7, and i don't get math at all. My mom isn't the greatest so i decided to try this for some help. My math problem is right now we are working on roots. I don't quite understand how to find the answer to the problems, i was wondering what is the easiest, and fastest way to find the answers to roots? Thank you!Hi,
In most cases, the best you can do when faced with finding a root is to approximate it. The "first approximation" comes from knowing those few values where you can find the root exactly. That is knowing the squares.
32 = 9
42 = 16
52 = 25
62 = 36
For values that are not prefect squares the best you can do is approximate the square root. For example, looking at the list above, 12 is between 9 and 16 so I know that the square root of 12 is between 3 and 4. This is my first approximation. For a second approximation I might try 3.5. Multiplying, 3.5 x 3.5 = 12.25 which is too large so the square root of 12 is between 3 and 3.5. This is my second approximation. I next tried 3.4, 3.4 x 3.4 = 11.56 which is too small so the square root of 12 is between 3.4 and 3.5. This is my third approximation.
A successive approximation algorithm of this type is explained more exactly in Approximating roots, the answer we gave to a previous question.
The fastest way to approximate a root is to use a calculator that has a square root button. The calculator uses an approximation method somewhat like the one dscribed above. This is one of the few places where we believe that a calculator is a useful tool in the classroom.Cheers,
Penny and Claude