Solution to

Estimating the Square Root of a Number Greater Than 1

Frame 5-27

The methods for estimating square root differs slightly depending upon

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whether the number is greater than 1 or less than 1. Let's begin with

numbers that are greater than 1.

(1) Pair off the digits of the number beginning at the decimal point

(or where the decimal point would be if the number had one)

and going to the left. Drop any digits to the right of the

decimal point.

(2) Identify the last digit or pair of digits (the digit or pair of digits

at the beginning of the number). If the number had an even

number of digits to the left of the decimal, you will have a pair

of digits. If the number had an odd number of digits to the left

of the decimal, you will have a single digit.

(a) If the digit/pair identified in step 2 is a perfect square

(1, 4, 9, 16, 25, 36, 49, 64, or 81), replace the digit/pair

with the square root of that digit/pair.

(b) If the digit/pair identified in step 2 is not a perfect square,

identify the largest perfect square that is less than the

digit/pair and replace the digit/pair with the square root of

that perfect square.

(3) For each **pair **of digits following the digit or digits identified in

step 2, substitute a zero.

(4) The resulting number is the estimated square root (low).

(5) Increase the left (first) digit of the estimated square root (low)

by 1 to arrive at the estimated square root (high).

(6) The actual square root will be less than the estimated square

root (high) and equal to or greater than the estimated square

root (low).

NOTE: If the digit/pair identified in step 2 is a perfect square and the

following pairs were all zeros originally and no non-zero digits followed

the decimal point of the original number, then the estimated square root

(low) is the actual square root.

Estimate the square root of the following numbers using the above rules.

a. 149,769

b. 640,000

c. 36,000

MD0900

5-17

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