# Square Root Day 2016: Going Back to Our Square Roots

Square Root Day is celebrated on days when both the day and the month are the square root (√) of the last two digits of the year. So this year it’s celebrated on 4/4/16 since 4 is the square root of 16. But what are square roots? When do we use them? And why? Square roots, often referred to as radicals, are a number that when multiplied by itself creates a new number—the root’s square (example: 2 is the square root of 4 because 2 × 2 = 4). We’ve collected 30 fun facts to answer these questions and more so that your classroom can get ready to celebrate square root day.

1. The square root of 2 is the same as the diagonal length of a square whose side length = 1. The square root of 3 is the diagonal of a cube whose side length = 1. Check out more square roots with this easy calculator.

2. The product of a number multiplied by itself is called a perfect square. The numbers multiplied to get that perfect square is its square root. This means that only rational (whole) numbers can be multiplied to create perfect squares.

3. The square root for a lot of numbers is irrational (not a whole integer). This can make it difficult to calculate in your head, but you can use a calculator or a table to find the square root of any number you want.

4. Here’s a quick trick for finding the length of the diagonal of a square. Just multiply one side of it by the square root of 2.

5. The Yale Babylonian Collection has a tablet from nearly 4,000 years ago that depicts the square root of 2 out to nine decimal places using a square and two diagonals. It also depicts 30√2, showing that square roots have been used for calculations for many thousands of years.

6. The Rhind Mathematical Papyrus is an Egyptian text from 1650 BCE that shows how the Ancient Egyptians were able to calculate square roots as well as perform many other mathematical processes that we still use today, such as calculating slopes and areas.

7. One way you can celebrate Square Root Day is by getting some of your favorite root vegetables and chopping them up into squares. Not a fan of veggies? No problem, get creative! How about fries or carrot cake to satisfy your square-root snacking needs?

8. Many imperfect squares repeat indefinitely. People have calculated square roots out to one million, two million, and even ten million decimal places!

9. Here’s a question for you: Why is this equation actually a mathematical limerick?

( (12 + 144 + 20 + 3 √4) / 7 ) + 5*11 = 92 + 0

Answer:

A dozen, a gross, and a score,

plus three times the square root of four,

divided by seven,

plus five times eleven,

is nine squared and not a bit more.

10. Ever wonder what a clock would look like if we used square roots instead of numbers?

11. Party square-root style with this square-root puzzle. If puzzles aren’t your cup of tea, online games like this square-root clock can also be a fun way to express your holiday spirit.

12. Communities in Ancient India were using square roots as early as 800 BCE. This is documented in the *Baudhayana Sulba Sutra, *one of a series of texts that cover subjects from religion to mathematics. The *Baudhayana Sulba Sutra *has close approximations of the square roots of 2 and 3. Another Ancient Indian text by Aryabhata called *Aryabhatiya *contained instructions for finding square roots for much larger numbers.

13. Aryabhata’s method was first introduced to Europe by the Italian architect Pietro di Giacomo Cataneo in 1546.

14. If you want to find square roots without using a calculator here’s a trick. Pick a number that when squared comes close to but less than the number you’re finding the square root of. For example if you’re finding the square root of 20 you’d choose 4 as the number you square. Then divide your number by the number you squared (20/4 = 5). Average your answer with the square root you used (5 and 4 average to 4.5). Keep repeating these steps until you get a number that when squared is close to the number you want the square root of.

15. There’s a pattern to which numbers end up being perfect squares. Here are the first ten perfect squares, see if you can figure it out: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

The answer is that each one increases by *n* + 2 where *n* is the amount that the last number increased. Example: 1 to 4 is +3, and 4 to 9 is +5 which is 3 + 2.

16. In 380 BCE Theaeteus introduced the Ancient Greeks to the idea that the square roots of positive whole numbers that are not perfect squares are irrational numbers—numbers that are not expressible as a fraction.

17. The square of odd numbers will always be odd, while the square of even numbers will always be even.

18. In the Chinese book, *Writings on Reckoning*, written in around 200 BCE during the Han Dynasty, a method for determining square roots is outlined. This is one of the oldest Chinese mathematical texts and outlines concepts such as calculating interest rates and finding volumes, in addition to determining square roots.

19. An Indian Mathematician from the 9th century named Mahāvīra is credited as the first person to state that negative square roots do not exist.

20. The Spiral of Theodorus was constructed by Theodorus of Cyrene in 500 BCE. He did this by calculating the square roots of successive right triangles. This discovery is documented in Plato’s *Theaetetus. *

21. Regiomontanus, a German noble, invented a new symbol for square roots in around 1450. Instead of the traditional √, Regiomontanus proposed that Germany use an elaborate R as an alternative square root symbol. This symbol was subsequently used by Italian scholar Gerolamo Cardano in his text, *Ars Magna*.

22. All perfect squares end in either 1, 4, 6, 9, 00, or 25. Although not all numbers ending in one of those numbers are perfect squares, you can be assured that numbers ending in 2, 3, 5 (but not 25), 7, 8, or 0 (but not 00) are not perfect squares.

23. Squares of two consecutive numbers differ by the sum of the two numbers. For example, if you know that 32 = 9, but want to determine what 42 is, all you have to do is add 3+4 to 9, and you’ll get that 42 = 16. See for yourself and try it with some other numbers.

24. The √ symbol was first used to represent taking a square root by Christoph Rudollf in his 1525 text, *Cross*. This was also the first text to use the + (plus) and – (minus) signs to represent addition and subtraction respectively.

25. So why are we celebrating Square Root Day to begin with? Square Root Day is actually the invention of a high school Drivers’ Education teacher from California named Ron Grodon. He’s been trying to get schools to celebrate Square Root Day since 1981, which if you ask me is pretty radical!

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