114 LearnersLast updated on May 26th, 2025
Square of 68
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 the topic, we will discuss the square of 68.
What is the Square of 68
The square of a number is the product of the number itself.
The square of 68 is 68 × 68.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 68², where 68 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 68 is 68 × 68 = 4624.
Square of 68 in exponential form: 68²
Square of 68 in arithmetic form: 68 × 68
How to Calculate the Value of Square of 68
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 68.
Step 1: Identify the number. Here, the number is 68.
Step 2: Multiplying the number by itself, we get, 68 × 68 = 4624.
The square of 68 is 4624.
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 68.
So: 68² = 68 × 68 = 4624
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 68.
Step 1: Enter the number in the calculator.
Enter 68 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×).
That is 68 × 68.
Step 3: Press the equal to button to find the answer. Here, the square of 68 is 4624.
Tips and Tricks for the Square of 68
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 68
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 68² with (6 + 8)² or (60 + 8)². So students should check and use the correct formula and double-check the answers to avoid all the confusion.
Mistake 3
Confusing 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 68
Problem 1
Find the length of the square, where the area of the square is 4624 cm².
The area of a square = a²
So, the area of a square = 4624 cm²
So, the length = √4624 = 68.
The length of each side = 68 cm
Explanation
The length of a square is 68 cm.
Because the area is 4624 cm² the length is √4624 = 68.
Problem 2
Alice is planning to tile her square garden of length 68 feet. The cost to tile a foot is 5 dollars. Then how much will it cost to tile the full garden?
The length of the garden = 68 feet
The cost to tile 1 square foot of garden = 5 dollars.
To find the total cost to tile, we find the area of the garden,
Area of the garden = area of the square = a²
Here a = 68
Therefore, the area of the garden = 68² = 68 × 68 = 4624.
The cost to tile the garden = 4624 × 5 = 23120.
The total cost = 23120 dollars
Explanation
To find the cost to tile the garden, we multiply the area of the garden by the cost to tile per foot. So, the total cost is 23120 dollars.
Problem 3
Find the area of a circle whose radius is 68 meters.
The area of the circle = 14526.56 m²
Explanation
The area of a circle = πr²
Here, r = 68
Therefore, the area of the circle = π × 68² = 3.14 × 68 × 68 = 14526.56 m².
Problem 4
The area of the square is 4624 cm². Find the perimeter of the square.
The perimeter of the square is 272 cm.
Explanation
The area of the square = a²
Here, the area is 4624 cm²
The length of the side is √4624 = 68
Perimeter of the square = 4a
Here, a = 68
Therefore, the perimeter = 4 × 68 = 272 cm.
Problem 5
Find the square of 69.
The square of 69 is 4761.
Explanation
The square of 69 is multiplying 69 by 69.
So, the square = 69 × 69 = 4761
FAQs on Square of 68
1.What is the square of 68?
2.What is the square root of 68?
3.Is 68 a prime number?
4.What are the first few multiples of 68?
5.What is the square of 67?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Square of 68?
8.How do technology and digital tools in Philippines support learning Algebra and Square of 68?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for Square 68.
- Even number: A number that is divisible by 2. For example, 2, 4, 6, 8, 10, etc.
- Perfect square: A number that is the square of an integer. For example, 1, 4, 9, 16, etc.
- Exponent: The number that indicates how many times the base is multiplied by itself. For example, in 2³, 3 is the exponent.
- Area: The measure of the surface of a shape. It is usually measured in square units.
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 144 is ±12.
Explore More algebra
![Important Math Links Icon]()
Previous to Square of 68
About BrightChamps in Philippines
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.
