Square of 1007
2026-02-28 23:47 Diff
https://brightchamps.com/en-us/math/algebra/square-of-1007

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Last updated on August 5, 2025

The product of multiplying an integer by itself is the square of a number. Square is used in programming, calculating areas, and so on. In the topic, we will discuss the square of 1007.

What is the Square of 1007

The square of a number is the product of the number itself. The square of 1007 is 1007 × 1007. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 1007², where 1007 is the base and 2 is the exponent. The square of a positive and a negative number is always positive.

For example, 5² = 25; -5² = 25.

The square of 1007 is 1007 × 1007 = 1,014,049.

Square of 1007 in exponential form: 1007²

Square of 1007 in arithmetic form: 1007 × 1007

How to Calculate the Value of the Square of 1007

The square of a number is multiplying the number by itself. So let’s learn how to find the square of a number. These are the common methods used to find the square of a number.

  • By Multiplication Method
  • Using a Formula
  • Using a Calculator

By the Multiplication Method

In this method, we will multiply the number by itself to find the square. The product here is the square of the number. Let’s find the square of 1007

Step 1: Identify the number. Here, the number is 1007

Step 2: Multiplying the number by itself, we get, 1007 × 1007 = 1,014,049.

The square of 1007 is 1,014,049.

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Using a Formula (a²)

In this method, the formula, a² is used to find the square of the number. Where a is the number.

Step 1: Understanding the equation

Square of a number = a²

a² = a × a

Step 2: Identifying the number and substituting the value in the equation.

Here, ‘a’ is 1007

So: 1007² = 1007 × 1007 = 1,014,049

By Using a Calculator

Using a calculator to find the square of a number is the easiest method. Let’s learn how to use a calculator to find the square of 1007.

Step 1: Enter the number in the calculator Enter 1007 in the calculator.

Step 2: Multiply the number by itself using the multiplication button (×) That is 1007 × 1007

Step 3: Press the equal to button to find the answer Here, the square of 1007 is 1,014,049.

Tips and Tricks for the Square of 1007

Tips and tricks make it easy for students to understand and learn the square of a number. To master the square of a number, these tips and tricks will help students.

  • The square of an even number is always an even number. For example, 6² = 36
     
  • The square of an odd number is always an odd number. For example, 5² = 25
     
  • The last digit of the square of a number is always 0, 1, 4, 5, 6, or 9.
     
  • If the square root of a number is a fraction or a decimal, then the number is not a perfect square. For example, √1.44 = 1.2
     
  • The square root of a perfect square is always a whole number. For example, √144 = 12.

Common Mistakes to Avoid When Calculating the Square of 1007

Mistakes are common among kids when doing math, especially when it is finding the square of a number. Let’s learn some common mistakes to master the squaring of a number.

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Problem 1

Find the length of the square, where the area of the square is 1,014,049 cm².

Okay, lets begin

The area of a square = a²

So, the area of a square = 1,014,049 cm²

So, the length = √1,014,049 = 1007.

The length of each side = 1007 cm

Explanation

The length of a square is 1007 cm. Because the area is 1,014,049 cm², the length is √1,014,049 = 1007.

Well explained 👍

Problem 2

Sarah is planning to tile her square courtyard of length 1007 feet. The cost to tile a foot is 5 dollars. Then how much will it cost to tile the full courtyard?

Okay, lets begin

The length of the courtyard = 1007 feet

The cost to tile 1 square foot of courtyard = 5 dollars.

To find the total cost to tile, we find the area of the courtyard,

Area of the courtyard = area of the square = a²

Here a = 1007

Therefore, the area of the courtyard = 1007²

= 1007 × 1007

= 1,014,049.

The cost to tile the courtyard = 1,014,049 × 5 = 5,070,245.

The total cost = 5,070,245 dollars

Explanation

To find the cost to tile the courtyard, we multiply the area of the courtyard by the cost to tile per foot. So, the total cost is 5,070,245 dollars.

Well explained 👍

Problem 3

Find the area of a circle whose radius is 1007 meters.

Okay, lets begin

The area of the circle = 3,183,947.66 m²

Explanation

The area of a circle = πr²

Here, r = 1007

Therefore, the area of the circle = π × 1007²

= 3.14 × 1007 × 1007

= 3,183,947.66 m².

Well explained 👍

Problem 4

The area of the square is 1,014,049 cm². Find the perimeter of the square.

Okay, lets begin

The perimeter of the square is 4028 cm.

Explanation

The area of the square = a²

Here, the area is 1,014,049 cm²

The length of the side is √1,014,049 = 1007

Perimeter of the square = 4a

Here, a = 1007

Therefore, the perimeter = 4 × 1007 = 4028.

Well explained 👍

Problem 5

Find the square of 1008.

Okay, lets begin

The square of 1008 is 1,016,064.

Explanation

The square of 1008 is multiplying 1008 by 1008. So, the square = 1008 × 1008 = 1,016,064.

Well explained 👍

FAQs on Square of 1007

1.What is the square of 1007?

The square of 1007 is 1,014,049, as 1007 × 1007 = 1,014,049.

2.What is the square root of 1007?

The square root of 1007 is approximately ±31.73.

3.Is 1007 a prime number?

No, 1007 is not a prime number; it is divisible by 19, 53, and other numbers.

4.What are the first few multiples of 1007?

The first few multiples of 1007 are 1007, 2014, 3021, 4028, 5035, 6042, 7049, 8056, and so on.

5.What is the square of 1006?

The square of 1006 is 1,012,036.

Important Glossaries for Square 1007.

  • Integer: A whole number that can be positive, negative, or zero but not a fraction or a decimal.
  • Exponent: The power to which a number is raised in exponential notation. For example, in 5², 2 is the exponent.
  • Perfect Square: A number that is the square of an integer. For example, 144 is a perfect square because it is 12².
  • Multiplication: The process of finding the total of one number added repeatedly a specified number of times.
  • Circle Area: The space contained within the circumference of a circle, calculated as πr², where r is the radius of the circle.

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.