Square of -21
2026-02-28 13:29 Diff
https://brightchamps.com/en-us/math/algebra/square-of-minus-21

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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 -21.

What is the Square of -21

The square of a number is the product of the number itself. The square of -21 is (-21) × (-21). The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as (-21)², where -21 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 -21 is (-21) × (-21) = 441.

Square of -21 in exponential form: (-21)²

Square of -21 in arithmetic form: (-21) × (-21)

How to Calculate the Value of Square of -21

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.

  1. By Multiplication Method
  2. Using a Formula
  3. 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 -21.

Step 1: Identify the number. Here, the number is -21

Step 2: Multiplying the number by itself, we get, (-21) × (-21) = 441.

The square of -21 is 441.

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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 -21 So: (-21)² = (-21) × (-21) = 441

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 -21.

Step 1: Enter the number in the calculator Enter -21 in the calculator.

Step 2: Multiply the number by itself using the multiplication button (×) That is (-21) × (-21)

Step 3: Press the equal to button to find the answer Here, the square of -21 is 441.

Tips and Tricks for the Square of -21: 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.
  • 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 -21

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.

Problem 1

Find the length of the square, where the area of the square is 441 cm².

Okay, lets begin

The area of a square = a²

So, the area of a square = 441 cm²

So, the length = √441 = 21.

The length of each side = 21 cm

Explanation

The length of a square is 21 cm. Because the area is 441 cm² the length is √441 = 21.

Well explained 👍

Problem 2

Tom is planning to paint his square wall of length -21 feet. The cost to paint a foot is 3 dollars. Can he paint the wall?

Okay, lets begin

The length of the wall = 21 feet

The cost to paint 1 square foot of wall = 3 dollars.

To find the total cost to paint, we find the area of the wall,

Area of the wall = area of the square = a²

Here a = 21

Therefore, the area of the wall = 21² = 21 × 21 = 441.

The cost to paint the wall = 441 × 3 = 1323.

The total cost = 1323 dollars

Explanation

To find the cost to paint the wall, we multiply the area of the wall by cost to paint per foot. So, the total cost is 1323 dollars.

Well explained 👍

Problem 3

Find the area of a circle whose radius is 21 meters.

Okay, lets begin

The area of the circle = 1,385.44 m²

Explanation

The area of a circle = πr²

Here, r = 21

Therefore, the area of the circle = π × 21² = 3.14 × 21 × 21 = 1,385.44 m².

Well explained 👍

Problem 4

The area of the square is 441 cm². Find the perimeter of the square.

Okay, lets begin

The perimeter of the square is 84 cm.

Explanation

The area of the square = a²

Here, the area is 441 cm²

The length of the side is √441 = 21

Perimeter of the square = 4a

Here, a = 21

Therefore, the perimeter = 4 × 21 = 84.

Well explained 👍

Problem 5

Find the square of -22.

Okay, lets begin

The square of -22 is 484.

Explanation

The square of -22 is multiplying -22 by -22. So, the square = (-22) × (-22) = 484

Well explained 👍

FAQs on Square of -21

1.What is the square of -21?

The square of -21 is 441, as (-21) × (-21) = 441.

2.What is the square root of 441?

The square root of 441 is ±21.

3.Is -21 a perfect square?

4.What are the first few multiples of 21?

The first few multiples of 21 are 21, 42, 63, 84, 105, 126, 147, 168, and so on.

5.What is the square of 20?

Important Glossaries for Square of -21.

  • Perfect square: A number that is the square of an integer. For example, 1, 4, 9, 16, 25, etc.
  • Exponent: The exponent of a number shows how many times the number is multiplied by itself. For example, in 3², 2 is the exponent.
  • Square root: The square root is the inverse operation of squaring a number. The square root of a number is a number whose square is the number itself.
  • Multiplication: An arithmetic operation that combines groups of equal sizes.
  • Integer: A whole number that can be positive, negative, or zero.

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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.