Pythagoras and SUMSQ

Ever heard of the philosopher and mathematician, Pythagoras of the 6th century BC? Perhaps you’ve come across one his most famous theorems during your geometry class. The Pythagorean Theorem states that in a right triangle, the sum of the legs squared is equal to the hypotenuse squared. 

Did you know that there is a spreadsheet function that can perform the Pythagorean Theorem – that is, calculate the square of the hypotenuse? The SUMSQ function can do just that: it will add up the squares of numbers!

Check out our 3-minute video below for an intro to SUMSQ and the Pythagoras function.

So, as shown in the video, if you have numbers 3 and 4, using the formula SUMSQ(3,4) will return 25. This is shown in Solution 2 in the embedded Google spreadsheet.

Now let’s verify this answer using the Pythagorean Theorem. Just as we’ve seen, let’s assume the legs of the right triangle are as follows:  a = 3 and b = 4. Using the Pythagorean Theorem, we find that 3-squared + 4-squared = 9 + 16 = 25. As shown in Solution 1, 25 is the answer to c-squared – and it matches the output of SUMSQ. So if you want to know the length of the hypotenuse (c), you simply have to take the square-root of 25, which is equal to 5!

[googleapps domain=”docs” dir=”spreadsheet/pub” query=”key=0ArU-OSCYb_YpdEZuS2oxb0tBUGNEQUpWQm9zQS1UWWc&output=html&widget=true” width=”500″ height=”300″ /]

Of course, the SUMSQ function is not limited to the Pythagorean Theorem and is not limited to 2 arguments. You can use this function to sum up the squares of as many numbers as you’d like. You can either directly include the number in the formula or include the cell that references your numbers.

Resources

• Spreadsheet: click here