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67 squared, (67)2, is the number you get when multiplying 67 times 67.
It can also be looked at as exponentiation involving the base 67 and the exponent 2.
The term is usually pronounced sixty-seven times sixty-seven or sixty-seven squared.
The square of 67 is a perfect square because the number is the product of the two equal integers 67.
It can be written as 67 × 67 or in exponential form.
Read on to learn everything about the number sixty-seven squared, including useful identities.
Calculator
(67)2 = 4,489
67 × 67 = 4,489
The inverse operation of squaring sixty-seven is extracting the square root of 67, explained here.
In the next section we elaborate on what is 67 squared and there you can also find our calculator.
What is 67 Squared?
A square is a flat shape with four equal sides; every angle is 90°.
Hence, a square with side length 67 has an area of 4,489.
67 squared equals the sum of the first 67 odd numbers:
In addition, the number can be calculated from 66 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(67)2 = 662 + 66 + 67 = 662 + 133 = 4,489
It can be also be computed from 66 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(67)2 = 2 x 662 – 652 + 2 = 2 x 4356 – 4225 + 2 = 4,489
The difference between the perfect square of 67 and its predecessor, 66, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 67 – 1 = 133 = (67)2 – 662 = 4,489 – 4356 = 133
67 is odd, and the square numbers of odd numbers are also odd: (2n + 1)2 = 4 × (n2 + n) + 1.
Squares of odd numbers like 67 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 67, you can use our calculator above.
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A square similar to 67 is, for example: square of 69.
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The following table contains the squares of numbers close to 67.
Table
Number | Square |
---|---|
62 | 3,844 |
63 | 3,969 |
64 | 4,096 |
65 | 4,225 |
66 | 4,356 |
67 | 4,489 |
68 | 4,624 |
69 | 4,761 |
70 | 4,900 |
71 | 5,041 |
72 | 5,184 |
Sixty-Seven Squared
By reading so far you know all about squaring the number 67 and calculating it using recursive methods, or as sum, product or by exponentiation.
67 squared is equivalent to 4,489.
If you were searching for what is 67 squared in math or if you typed whats 67 squared in the search engine you now have all the answers, too.
The same goes for searches like square67, and 67 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 67 squared using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
67 squared = 67 × 67 = (67)2 = 4,489.
The exponentiation form is mostly used to denote sixty-seven squared.
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– Article written by Mark, last updated on November 26th, 2023