Square of 1001
2026-02-28 23:12 Diff
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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 this topic, we will discuss the square of 1001.

What is the Square of 1001

The square of a number is the product of the number itself. The square of 1001 is 1001 × 1001. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as \(1001^2\), where 1001 is the base and 2 is the exponent. The square of a positive and a negative number is always positive.

For example, (52 = 25); ((-5)2 = 25).

The square of 1001 is 1001 × 1001 = 1,002,001.

Square of 1001 in exponential form: (10012)

Square of 1001 in arithmetic form: 1001 × 1001

How to Calculate the Value of Square of 1001

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 1001.

Step 1: Identify the number. Here, the number is 1001.

Step 2: Multiplying the number by itself, we get, 1001 × 1001 = 1,002,001.

The square of 1001 is 1,002,001.

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Using a Formula (\(a^2\))

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 1001.

So: (10012 = 1001 × 1001 = 1,002,001)

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 1001.

Step 1: Enter the number in the calculator. Enter 1001 in the calculator.

Step 2: Multiply the number by itself using the multiplication button(×). That is 1001 × 1001.

Step 3: Press the equal button to find the answer. Here, the square of 1001 is 1,002,001.

Tips and Tricks for the Square of 1001

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, (sqrt{1.44} = 1.2).
     
  • The square root of a perfect square is always a whole number. For example, (sqrt{144} = 12).

Common Mistakes to Avoid When Calculating the Square of 1001

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

A square garden has an area of 1,002,001 square meters. What is the length of one side of the garden?

Okay, lets begin

The area of a square = (a2)

So, the area of the square = 1,002,001 m2

So, the length = (sqrt{1,002,001} = 1001).

The length of each side = 1001 m

Explanation

The length of a square garden is 1001 meters. Because the area is 1,002,001 m2, the length is (sqrt{1,002,001} = 1001).

Well explained 👍

Problem 2

Sarah is fencing her square field with a side length of 1001 feet. The cost to fence one foot is 5 dollars. How much will it cost to fence the entire field?

Okay, lets begin

The length of the field = 1001 feet

The cost to fence 1 foot of the field = 5 dollars.

To find the total cost to fence, we find the perimeter of the field,

Perimeter of the field = 4 × side length

Here side length = 1001

Therefore, the perimeter = 4 × 1001 = 4004.

The cost to fence the field = 4004 × 5 = 20,020.

The total cost = 20,020 dollars

Explanation

To find the cost to fence the field, we multiply the perimeter of the field by the cost to fence per foot. So, the total cost is 20,020 dollars.

Well explained 👍

Problem 3

Find the area of a circle whose radius is 1001 meters.

Okay, lets begin

The area of the circle = 3,146,127.64 m2

Explanation

The area of a circle = (pi r2)

Here, r = 1001

Therefore, the area of the circle = (pi × 10012 ) ≈ (3.14 × 1001 × 1001 = 3,146,127.64) m2.

Well explained 👍

Problem 4

A square plot has an area of 1,002,001 square feet. Find the perimeter of the plot.

Okay, lets begin

The perimeter of the plot is 4,004 feet.

Explanation

The area of the square = (a2)

Here, the area is 1,002,001 ft2

The length of the side is (sqrt{1,002,001} = 1001)

Perimeter of the square = 4a

Here, a = 1001

Therefore, the perimeter = 4 × 1001 = 4004.

Well explained 👍

Problem 5

Find the square of 1002.

Okay, lets begin

The square of 1002 is 1,004,004

Explanation

The square of 1002 is multiplying 1002 by 1002. So, the square = 1002 × 1002 = 1,004,004

Well explained 👍

FAQs on Square of 1001

1.What is the square of 1001?

The square of 1001 is 1,002,001, as 1001 × 1001 = 1,002,001.

2.What is the square root of 1001?

The square root of 1001 is approximately ±31.64.

3.Is 1001 a prime number?

No, 1001 is not a prime number; it is divisible by 7, 11, and 13.

4.What are the first few multiples of 1001?

The first few multiples of 1001 are 1001, 2002, 3003, 4004, 5005, and so on.

5.What is the square of 1000?

The square of 1000 is 1,000,000.

Important Glossaries for Square 1001.

  • Prime number: A number that is only divisible by 1 and itself. For example, 2, 3, 5, 7, 11, etc.
  • Exponential form: A way of expressing numbers as a base raised to a power. For example, (92) where 9 is the base and 2 is the power.
  • Square root: The number that, when multiplied by itself, gives the original number. For example, (sqrt{144} = 12).
  • Multiplication method: A method to find the square of a number by multiplying it by itself.
  • Perfect square: A number that has an integer as its square root. For example, 144 is a perfect square because its square root is 12.

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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.