130 LearnersLast updated on May 29th, 2025
Square of 314
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 314.
What is the Square of 314
The square of a number is the product of the number by itself.
The square of 314 is 314 × 314.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 314², where 314 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 314 is 314 × 314 = 98,596.
Square of 314 in exponential form: 314²
Square of 314 in arithmetic form: 314 × 314
How to Calculate the Value of Square of 314
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 314
Step 1: Identify the number. Here, the number is 314
Step 2: Multiplying the number by itself, we get, 314 × 314 = 98,596.
The square of 314 is 98,596.
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 314
So: 314² = 314 × 314 = 98,596
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 314.
Step 1: Enter the number in the calculator. Enter 314 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 314 × 314
Step 3: Press the equal to button to find the answer Here, the square of 314 is 98,596.
Tips and Tricks for the Square of 314
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 314
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 will be using the formula.
The formula to find the square of the number is a². Instead, students may use 314² with (3 +14)² or (310 + 4)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.
Solved Examples on Square of 314
Problem 1
Find the side length of a square plot whose area is 98,596 m².
The area of a square = a² So, the area of a square = 98,596 m² So, the side length = √98,596 = 314. The side length of each side = 314 m
Explanation
The side length of a square is 314 m.
Because the area is 98,596 m², the side length is √98,596 = 314.
Problem 2
A square garden has a side length of 314 feet. The cost to fence a foot is 5 dollars. How much will it cost to fence the entire garden?
The side length of the garden = 314 feet
The cost to fence 1 foot of the garden = 5 dollars.
To find the total cost to fence, we find the perimeter of the garden.
Perimeter of the garden = 4a
Here a = 314
Therefore, the perimeter = 4 × 314 = 1,256.
The cost to fence the garden = 1,256 × 5 = 6,280.
The total cost = 6,280 dollars.
Explanation
To find the cost to fence the garden, we multiply the perimeter of the garden by the cost to fence per foot. So, the total cost is 6,280 dollars.
Problem 3
Find the area of a circle whose radius is 314 meters.
The area of the circle = 309,760.06 m²
Explanation
The area of a circle = πr²
Here, r = 314
Therefore, the area of the circle = π × 314² = 3.14 × 314 × 314 = 309,760.06 m².
Problem 4
The area of a square is 98,596 cm². Find the perimeter of the square.
The perimeter of the square is 1,256 cm
Explanation
The area of the square = a²
Here, the area is 98,596 cm²
The length of the side is √98,596 = 314
Perimeter of the square = 4a
Here, a = 314
Therefore, the perimeter = 4 × 314 = 1,256.
Problem 5
Find the square of 315.
The square of 315 is 99,225
Explanation
The square of 315 is multiplying 315 by 315.
So, the square = 315 × 315 = 99,225
FAQs on Square of 314
1.What is the square of 314?
2.What is the square root of 314?
3.Is 314 a prime number?
4.What are the first few multiples of 314?
5.What is the square of 313?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square of 314?
8.How do technology and digital tools in India support learning Algebra and Square of 314?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for Square 314.
- Perfect Square: A number that is the square of an integer. For example, 121 is a perfect square as it is 11².
- Even Number: A number divisible by 2 without a remainder. For example, 4, 6, 8, etc.
- Prime Number: A natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, 7, 11, etc.
- Exponential Form: A way of expressing a number as a base raised to a power. For example, 3² is the exponential form of 9.
- Square Root: The number that produces a specified quantity when multiplied by itself. For example, the square root of 25 is 5.
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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
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