121 LearnersLast updated on May 26th, 2025
Square of 852
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 852.
What is the Square of 852
The square of a number is the product of the number itself. The square of 852 is 852 × 852. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 852², where 852 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 852 is 852 × 852 = 726,804.
Square of 852 in exponential form: 852²
Square of 852 in arithmetic form: 852 × 852
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How to Calculate the Value of Square of 852
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 852.
Step 1: Identify the number. Here, the number is 852.
Step 2: Multiplying the number by itself, we get, 852 × 852 = 726,804.
The square of 852 is 726,804.
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 852. So: 852² = 852 × 852 = 726,804
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 852.
Step 1: Enter the number in the calculator Enter 852 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is 852 × 852
Step 3: Press the equal to button to find the answer Here, the square of 852 is 726,804.
Tips and Tricks for the Square of 852
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 852
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.
Mistake 1
Calculation errors:
Calculation errors mostly happen when students skip the steps or else by swapping the digits. To avoid it, students should double-check the answer. They can double-check by finding the square root of the solution they found. For example, the square of 25 is 625, and the square root of 625 is ±25.
Mistake 2
Errors when using the formula.
The formula to find the square of the number is a². Instead, students may use 852² with (8+5+2)² or (800+50+2)². So students should check and use the correct formula and double-check the answers to avoid all the confusion.
Mistake 3
Confusing with square and square root.
Not understanding the concept of square and square root can lead to confusion in students. To avoid it, students should understand the concept that square and square root are inverse operations. The square of 5 is 25, and the square root of 25 is ±5.
Mistake 4
Errors in parentheses.
Ignoring the parentheses when finding the square of a number can lead to errors. So, students should understand parentheses and do the operations in the correct order to avoid error.
Mistake 5
Not practicing regularly.
Regular practice is required to master the square of a number. So students should do regular practice to avoid errors.
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Solved Examples on Square of 852
Problem 1
Find the length of the square, where the area of the square is 726,804 cm².
The area of a square = a²
So, the area of a square = 726,804 cm²
So, the length = √726,804 = 852.
The length of each side = 852 cm
Explanation
The length of a square is 852 cm.
Because the area is 726,804 cm², the length is √726,804 = 852.
Problem 2
Linda is planning to carpet her square room with a length of 852 feet. The cost to carpet a square foot is 2 dollars. How much will it cost to carpet the entire room?
The length of the room = 852 feet
The cost to carpet 1 square foot of the room = 2 dollars.
To find the total cost to carpet, we find the area of the room,
Area of the room = area of the square = a²
Here a = 852
Therefore, the area of the room = 852² = 852 × 852 = 726,804.
The cost to carpet the room = 726,804 × 2 = 1,453,608.
The total cost = 1,453,608 dollars
Explanation
To find the cost to carpet the room, we multiply the area of the room by the cost to carpet per foot. So, the total cost is 1,453,608 dollars.
Problem 3
Find the area of a circle whose radius is 852 meters.
The area of the circle = 2,279,853.28 m²
Explanation
The area of a circle = πr²
Here, r = 852
Therefore, the area of the circle = π × 852² = 3.14 × 852 × 852 = 2,279,853.28 m².
Problem 4
The area of the square is 726,804 cm². Find the perimeter of the square.
The perimeter of the square is
Explanation
The area of the square = a²
Here, the area is 726,804 cm²
The length of the side is √726,804 = 852
Perimeter of the square = 4a
Here, a = 852
Therefore, the perimeter = 4 × 852 = 3,408.
Problem 5
Find the square of 853.
The square of 853 is 727,609
Explanation
The square of 853 is multiplying 853 by 853. So, the square = 853 × 853 = 727,609
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FAQs on Square of 852
1.What is the square of 852?
2.What is the square root of 852?
3.Is 852 a perfect square?
4.What are the first few multiples of 852?
5.What is the square of 851?
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Important Glossaries for Square of 852
- Perfect square: A number that is the square of an integer. For example, 4, 9, 16, etc.
- Exponential form: Exponential form is the way of writing a number in the form of a power. For example, 9² where 9 is the base and 2 is the power.
- Square root: The square root is the inverse operation of the square. The square root of a number is a number whose square is the number itself.
- Even number: An integer that is exactly divisible by 2. For example, 2, 4, 6, etc.
- Odd number: An integer that is not divisible by 2. For example, 1, 3, 5, etc.
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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.
