130 LearnersLast updated on May 27th, 2025
Square of 784
The product of multiplying an integer by itself is the square of a number. The square is used in programming, calculating areas, and so on. In this topic, we will discuss the square of 784.
What is the Square of 784
The square of a number is the product of the number with itself.
The square of 784 is 784 × 784.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 784², where 784 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 784 is 784 × 784 = 614656.
Square of 784 in exponential form: 784²
Square of 784 in arithmetic form: 784 × 784
How to Calculate the Value of Square of 784
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 multiply the number by itself to find the square. The product here is the square of the number. Let’s find the square of 784.
Step 1: Identify the number. Here, the number is 784.
Step 2: Multiplying the number by itself, we get, 784 × 784 = 614656.
The square of 784 is 614656.
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 784. So: 784² = 784 × 784 = 614656
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 784.
Step 1: Enter the number in the calculator. Enter 784 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 784 × 784.
Step 3: Press the equal to button to find the answer. Here, the square of 784 is 614656.
Tips and Tricks for the Square of 784
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 784
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 784² with (7 + 8 + 4)² or (700 + 84)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 784
Problem 1
Find the length of the square, where the area of the square is 614656 cm².
The area of a square = a²
So, the area of a square = 614656 cm²
So, the length = √614656 = 784.
The length of each side = 784 cm
Explanation
The length of a square is 784 cm.
Because the area is 614656 cm², the length is √614656 = 784.
Problem 2
Sarah is planning to tile her square floor of length 784 feet. The cost to tile a square foot is 2 dollars. Then how much will it cost to tile the full floor?
The length of the floor = 784 feet
The cost to tile 1 square foot of the floor = 2 dollars.
To find the total cost to tile, we find the area of the floor, Area of the floor = area of the square = a²
Here a = 784
Therefore, the area of the floor = 784² = 784 × 784 = 614656.
The cost to tile the floor = 614656 × 2 = 1229312.
The total cost = 1229312 dollars
Explanation
To find the cost to tile the floor, we multiply the area of the floor by the cost to tile per foot.
So, the total cost is 1229312 dollars.
Problem 3
Find the area of a circle whose radius is 784 meters.
The area of the circle = 1,932,256.64 m²
Explanation
The area of a circle = πr²
Here, r = 784
Therefore, the area of the circle = π × 784² = 3.14 × 784 × 784 = 1,932,256.64 m².
Problem 4
The area of the square is 614656 cm². Find the perimeter of the square.
The perimeter of the square is 3136 cm.
Explanation
The area of the square = a²
Here, the area is 614656 cm²
The length of the side is √614656 = 784
Perimeter of the square = 4a
Here, a = 784
Therefore, the perimeter = 4 × 784 = 3136.
Problem 5
Find the square of 785.
The square of 785 is 616225.
Explanation
The square of 785 is multiplying 785 by 785.
So, the square = 785 × 785 = 616225.
FAQs on Square of 784
1.What is the square of 784?
2.What is the square root of 784?
3.Is 784 a perfect square?
4.What are the first few multiples of 784?
5.What is the square of 783?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Square of 784?
8.How do technology and digital tools in Canada support learning Algebra and Square of 784?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for Square 784.
- Perfect square: A number that is the square of an integer. For example, 784 is a perfect square because √784 = 28.
- Exponential form: A way of writing numbers using a base and an exponent, such as 784².
- Square root: The number which, when multiplied by itself, gives the original number. For example, the square root of 784 is 28.
- Multiplication method: A method to find the square by multiplying the base number by itself.
- Calculator method: Using a calculator to directly compute the square by entering the number and using the square or multiplication function.
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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.
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