How do you find the positive square root of 44100?

Answer 1

Various methods:

1: Use the square root function of a spreadsheet:

Into a cell enter the formula =SQRT(44100)

2: Use the square root function on a calculator; depending upon calculator:

[√] [4] [4] [1] [0] [0] [=]

or [4] [4] [1] [0] [0] [√]

3: Use a slide rule:

44100 = 4.41 × 10^4 → √44100 = √(4.41 × 10^4) = √4.41 × √(10^4) = √4.41 × 10²

So put the cursor over 4.41 on the A or B scale, read the square root off the D or C scale and multiply it by 100.

4: Use log tables, base 10 being the easiest:

44100 = 4.41 × 10^4

Using logs to base 10, look up 4.41 and add 4.

Divide this by 2.

Remove and remember the whole number (which will be 2).

Look up the remaining decimal number (either in the log table or an anti-log table) and multiply this by 10^(the removed whole number) = 10^2 = 100.

5: Use a kind of long division:

5.1 Split the number into pairs of digits from the right hand end (there may be a single digit in the first pair of digits at the left hand end);

5.2 Start with the first pair of digits at the left hand end as the first number under consideration and a quotient of 0;

5.3 Multiply the quotient so far by 20; Now find the largest single digit which when added to this and then this sum is multiplied by this digit is less than or equal to the number under consideration;

5.4 Write this digit over the pair of digits (as the next digit of the quotient);

5.5 Subtract the sum multiplied by the digit from the number under consideration;

5.6 Bring down the next pair of digits (just like brining down the next digit in normal long division) to form the next number under consideration.

5.7 Repeat from step 5.3 until all the pairs of digits have been used up.

6: Use knowledge:

44100 = 441 × 100

→ √44100 = √(441 × 100) = √441 × √100 = 21 × 10 = 210

Knowing that 441 is 21² and thus √441 = √(21²) = 21.