Table of Contents
3 squared, (3)2, is the number you get when multiplying 3 times 3.
It can also be looked at as exponentiation involving the base 3 and the exponent 2.
The term is usually pronounced three times three or three squared.
The square of 3 is a perfect square because the number is the product of the two equal integers 3.
It can be written as 3 × 3 or in exponential form.
Read on to learn everything about the number three squared, including useful identities.
Calculator
(3)2 = 9
3 × 3 = 9
The inverse operation of squaring three is extracting the square root of 3, explained here.
In the next section we elaborate on what is 3 squared and there you can also find our calculator.
What is 3 Squared?
A square is a flat shape with four equal sides; every angle is 90°.
Hence, a square with side length 3 has an area of 9.
3 squared equals the sum of the first 3 odd numbers:
In addition, the number can be calculated from 2 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(3)2 = 22 + 2 + 3 = 22 + 5 = 9
It can be also be computed from 2 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(3)2 = 2 x 22 – 12 + 2 = 2 x 4 – 1 + 2 = 9
The difference between the perfect square of 3 and its predecessor, 2, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 3 – 1 = 5 = (3)2 – 22 = 9 – 4 = 5
3 is odd, and the square numbers of odd numbers are also odd: (2n + 1)2 = 4 × (n2 + n) + 1.
Squares of odd numbers like 3 are of the form 8n + 1, because (2n + 1)2 = 4n × (n + 1) + 1;
n × (n + 1) is an even number.
If you want to calculate the square of any number, not only integers like 3, you can use our calculator above.
Enter your number; nothing else to be done.
A square similar to 3 is, for example: square of 5.
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The following table contains the squares of numbers close to 3.
Table
| Number | Square |
|---|---|
| -2 | 4 |
| -1 | 1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
| 6 | 36 |
| 7 | 49 |
| 8 | 64 |
Three Squared
By reading so far you know all about squaring the number 3 and calculating it using recursive methods, or as sum, product or by exponentiation.
3 squared is equivalent to 9.
If you were searching for what is 3 squared in math or if you typed whats 3 squared in the search engine you now have all the answers, too.
The same goes for searches like square3, and 3 to the 2nd power, just to name a few more examples people are often looking for.
Note that you can also find many perfect squares including 3 squared using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
3 squared = 3 × 3 = (3)2 = 9.
The exponentiation form is mostly used to denote three squared.
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– Article written by Mark, last updated on November 26th, 2023