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1000 squared, (1000)2, is the number you get when multiplying 1000 times 1000.
It can also be looked at as exponentiation involving the base 1000 and the exponent 2.
The term is usually pronounced one thousand times one thousand or one thousand squared.
The square of 1000 is a perfect square because the number is the product of the two equal integers 1000.
It can be written as 1000 × 1000 or in exponential form.
Read on to learn everything about the number one thousand squared, including useful identities.
Calculator
(1000)2 = 1,000,000
1000 × 1000 = 1,000,000
The inverse operation of squaring one thousand is extracting the square root of 1000, explained here.
In the next section we elaborate on what is 1000 squared and there you can also find our calculator.
What is 1000 Squared?
A square is a flat shape with four equal sides; every angle is 90°.
Hence, a square with side length 1000 has an area of 1,000,000.
1000 squared equals the sum of the first 1000 odd numbers:
In addition, the number can be calculated from 999 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(1000)2 = 9992 + 999 + 1000 = 9992 + 1999 = 1,000,000
It can be also be computed from 999 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(1000)2 = 2 x 9992 – 9982 + 2 = 2 x 998001 – 996004 + 2 = 1,000,000
The difference between the perfect square of 1000 and its predecessor, 999, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 1000 – 1 = 1999 = (1000)2 – 9992 = 1,000,000 – 998001 = 1999
1000 is even, and the square numbers of even numbers are also even: (2n)2 = 4n2.
Squares of even numbers like 1000 are divisible by 4 for
= n2.
If you want to calculate the square of any number, not only integers like 1000, you can use our calculator above.
Enter your number; nothing else to be done.
A square similar to 1000 is, for example: square of 1002.
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The following table contains the squares of numbers close to 1000.
Table
| Number | Square |
|---|---|
| 995 | 990,025 |
| 996 | 992,016 |
| 997 | 994,009 |
| 998 | 996,004 |
| 999 | 998,001 |
| 1000 | 1,000,000 |
| 1001 | 1,002,001 |
| 1002 | 1,004,004 |
| 1003 | 1,006,009 |
| 1004 | 1,008,016 |
| 1005 | 1,010,025 |
One Thousand Squared
By reading so far you know all about squaring the number 1000 and calculating it using recursive methods, or as sum, product or by exponentiation.
1000 squared is equivalent to 1,000,000.
If you were searching for what is 1000 squared in math or if you typed whats 1000 squared in the search engine you now have all the answers, too.
The same goes for searches like square1000, and 1000 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 1000 squared using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
1000 squared = 1000 × 1000 = (1000)2 = 1,000,000.
The exponentiation form is mostly used to denote one thousand squared.
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– Article written by Mark, last updated on November 26th, 2023