128 LearnersLast updated on May 29th, 2025
Square of 312
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 312.
What is the Square of 312
The square of a number is the product of the number itself.
The square of 312 is 312 × 312.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 312², where 312 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 312 is 312 × 312 = 97344.
Square of 312 in exponential form: 312²
Square of 312 in arithmetic form: 312 × 312
How to Calculate the Value of Square of 312
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 (a2)
- 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 312.
Step 1: Identify the number. Here, the number is 312.
Step 2: Multiplying the number by itself, we get, 312 × 312 = 97344.
The square of 312 is 97344.
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 312.
So: 312² = 312 × 312 = 97344
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 312.
Step 1: Enter the number in the calculator. Enter 312 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 312 × 312
Step 3: Press the equal to button to find the answer Here, the square of 312 is 97344.
Tips and Tricks for the Square of 312
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 312
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 while using the formula.
The formula to find the square of the number is a². Instead, students may use 312² with (3 + 12)² or (300 + 12)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 errors.
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.
Solved Examples on Square of 312
Problem 1
Find the length of the square, where the area of the square is 97344 cm².
The area of a square = a²
So, the area of a square = 97344 cm²
So, the length = √97344 = 312.
The length of each side = 312 cm
Explanation
The length of a square is 312 cm.
Because the area is 97344 cm², the length is √97344 = 312.
Problem 2
Samantha is planning to paint her square ceiling of length 312 feet. The cost to paint a foot is 5 dollars. Then how much will it cost to paint the full ceiling?
The length of the ceiling = 312 feet
The cost to paint 1 square foot of ceiling = 5 dollars.
To find the total cost to paint, we find the area of the ceiling.
Area of the ceiling = area of the square = a²
Here a = 312
Therefore, the area of the ceiling = 312² = 312 × 312 = 97344.
The cost to paint the ceiling = 97344 × 5 = 486720.
The total cost = 486720 dollars
Explanation
To find the cost to paint the ceiling, we multiply the area of the ceiling by the cost to paint per foot. So, the total cost is 486720 dollars.
Problem 3
Find the area of a circle whose radius is 312 meters.
The area of the circle = 305258.88 m²
Explanation
The area of a circle = πr²
Here, r = 312
Therefore, the area of the circle = π × 312² = 3.14 × 312 × 312 = 305258.88 m².
Problem 4
The area of the square is 97344 cm². Find the perimeter of the square.
The perimeter of the square is 1248 cm.
Explanation
The area of the square = a²
Here, the area is 97344 cm²
The length of the side is √97344 = 312
Perimeter of the square = 4a
Here, a = 312
Therefore, the perimeter = 4 × 312 = 1248.
Problem 5
Find the square of 313.
The square of 313 is 97969.
Explanation
The square of 313 is multiplying 313 by 313.
So, the square = 313 × 313 = 97969.
FAQs on Square of 312
1.What is the square of 312?
2.What is the square root of 312?
3.Is 312 a perfect square?
4.What are the first few multiples of 312?
5.What is the square of 311?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square of 312?
8.How do technology and digital tools in Qatar support learning Algebra and Square of 312?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for Square of 312.
- Perfect square: A number that is the square of an integer. For example, 36 is a perfect square because it is 6².
- Exponential form: Exponential form is a way of writing numbers using a base and an exponent. For example, 9² where 9 is the base and 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 value that, when multiplied by itself, gives the original number.
- Multiplication: An arithmetic operation that represents combining groups of equal sizes.
- Integer: A whole number that can be positive, negative, or zero, but not a fraction.
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About BrightChamps in Qatar
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.
