If 20x20=400 and 7x7=49, why doesn't 27x27=449?

This is my 449th post in the Excel Math blog, where we investigate ways that adults can use math they learned in elementary school.

As I have been approaching the 450th blog, I started to think about what I could write about. Maybe squares and square roots? (although squares are often tackled in middle school math).

In my head I started to calculate the square root of 450 - it's more than 20 squared (400) and less than 25 (I know from memory that's 625). I got my calculator out and learned that the square root of 450 is ~ 21.21.

Suddenly I dropped all thought of 450 and decided to focus on getting blog post #449 finished. This is today's deadline; this blog is a daily task and tomorrow can take care of itself. (That comes from Matthew 6:34 in the Bible and doesn't help me solve #449, so maybe I'll save it for blog 634). Now back to the math.

Maybe 449 has an even square root? This sounds right to me:

• If 20 x 20 = 400 and 7 x 7 = 49, then 27 x 27 = 449 Right?

No!  Why?  Because. No matter how badly you want it to be. Not even if you wish on a star, it isn't.

Sadly, the square root of 449 is ~ 21.19, just a tiny bit lower than the square root of 450.

Math answers do not exist to please us - they exist as a consequence of the rules of numerical behavior. Who set the rules? The people who throughout history have "proved" how math works.

It's true that

• Twenty times twenty equals 400, and
• Seven times seven equals 49

However,

• Twenty-seven times twenty-seven equals 729
• Twenty times twenty-seventy equals 540
• Seven times twenty-seven equals 189
• Those two numbers added together do equal 729 (it's a long way from 449)

Why do those two calculations add up to the square of 27 and the other numbers didn't?

That's too long an answer for this blog, but I can say this:

Just wishing for something doesn't make it so. Even if we wish fervently.

If it did, we would all score higher on math tests ... get admitted to any program we apply to ...  reach our sales targets ... and in card games we would always win.

Fervently: exhibiting particular enthusiasm, zeal, conviction, persistence, or belief; having or showing emotional warmth, fervor, or passion