High/low Method
A simple way to compute a square root is the high/low method, similar to the bisection method. This method involves guessing a number based on known squares, then checking if its square is too high or too low and adjusting accordingly.
To find the square root of 20, first note that 42 is 16, and that 52 is 25. As 16 < 20 < 25, the square root of 20 must be between 4 and 5. Guessing 4.5 yields 20.25 and is too high. The next step is to guess 4.4, yielding 19.36 and is too low. Therefore, as before, the square root of 20 must be in between 4.4 and 4.5. This pattern is continued until the desired number of decimal places is achieved. For example:
- 4.452 = 19.8025 (too low)
- 4.472 = 19.9809 (too low, but close)
- 4.482 = 20.0704 (too high)
- 4.4752 = 20.025625 (too high)
- 4.4732 = 20.007729 (too high)
- 4.4722 = 19.998784 (too low, but close)
Now it is known that the square root of 20 is between 4.472 and 4.473, so the decimal representation begins with 4.472...
Read more about this topic: Methods Of Computing Square Roots
Famous quotes containing the words high and/or method:
“There is a sort of homely truth and naturalness in some books which is very rare to find, and yet looks cheap enough. There may be nothing lofty in the sentiment, or fine in the expression, but it is careless country talk. Homeliness is almost as great a merit in a book as in a house, if the reader would abide there. It is next to beauty, and a very high art. Some have this merit only.”
—Henry David Thoreau (1817–1862)
“Letters are above all useful as a means of expressing the ideal self; and no other method of communication is quite so good for this purpose.... In letters we can reform without practice, beg without humiliation, snip and shape embarrassing experiences to the measure of our own desires....”
—Elizabeth Hardwick (b. 1916)