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How To Square and Square Root Numbers

This article explains the symbols used to define the square of a number and the square root of a number. The explanation applies to calculating the length of a piece of lumber needed for a stair stringer as required in building stairs. However, the information is relevant anytime one needs to find the square or square root of a number.

When you see an elevated "2" (102) at the end of a number it means that the number is to be multiplied by itself:

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As an example:

In mathematical terms a number which is presented as 102 means that you are to multiply the number 10 by the number 10.

102 could also be written as 10 X 10

When you see a square root symbol (√) it means that the number is what number multiplied by itself would equal that number.

As an example:

√100 would be 10, because 10 x 10 equals 100.

In the stair calculation for the length of the lumber necessary to make a stringer, the formula is:

Total Rise2 + Total Run2 = Length of Stringer2

The formula could also be written as:

(Total Rise X Total Rise) + (Total Run X Total Run) = Length of Stringer X Length of Stringer

Or, based on our specific example

(106.75 X 106.75) + (140 X 140) = 30,995

Or

106.752 X 1402 = 30,995

To complete the stair stringer length calculation we need to know what number multiplied by itself will equal 30,995.

The square root of 30,995 is 176.054

Note: Finding the square root of a number can be done manually. However, most calculators and spreadsheets have a square root calculation function! In Microsoft Excel the function is SQRT. If you go to a cell in an Excel spreadsheet and enter; =SQRT(30995) you will end up with a resultant of 176.054

This number is the length of the stringer in inches. Hence to make it into feet we divide the number by 12:

176.054 รท 12 = 14.67 feet.

0.67 of a foot is 8 inches. This is determined by multiplying 12 (the number of inches in a foot) X 0.67 (the fraction amount of feet that we have from our calculation), which equals 8.