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!


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.

22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
Hence you know that the square root of 16 is 4, and the square root of 36 is 6.

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.

Penny and Claude
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