129 LearnersLast updated on May 29th, 2025
Square of 1764
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 1764.
What is the Square of 1764
The square of a number is the product of the number itself.
The square of 1764 is 1764 × 1764.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 1764², where 1764 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 1764 is 1764 × 1764 = 3,111,696.
Square of 1764 in exponential form: 1764²
Square of 1764 in arithmetic form: 1764 × 1764
How to Calculate the Value of Square of 1764
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 1764.
Step 1: Identify the number. Here, the number is 1764.
Step 2: Multiplying the number by itself, we get, 1764 × 1764 = 3,111,696.
The square of 1764 is 3,111,696.
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 1764.
So: 1764² = 1764 × 1764 = 3,111,696.
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 1764.
Step 1: Enter the number in the calculator. Enter 1764 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 1764 × 1764
Step 3: Press the equal to button to find the answer. Here, the square of 1764 is 3,111,696.
Tips and Tricks for the Square of 1764
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 1764
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 1764² with (1000 + 764)² or (1700 + 64)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 1764
Problem 1
Find the length of the square, where the area of the square is 3,111,696 cm².
The area of a square = a²
So, the area of a square = 3,111,696 cm²
So, the length = √3,111,696 = 1764.
The length of each side = 1764 cm
Explanation
The length of a square is 1764 cm.
Because the area is 3,111,696 cm², the length is √3,111,696 = 1764.
Problem 2
Emma is planning to carpet her square room of length 1764 feet. The cost to carpet a foot is 5 dollars. Then how much will it cost to carpet the full room?
The length of the room = 1764 feet
The cost to carpet 1 square foot of room = 5 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 = 1764
Therefore, the area of the room = 1764² = 1764 × 1764 = 3,111,696.
The cost to carpet the room = 3,111,696 × 5 = 15,558,480.
The total cost = 15,558,480 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 15,558,480 dollars.
Problem 3
Find the area of a circle whose radius is 1764 meters.
The area of the circle = 9,779,764.56 m²
Explanation
The area of a circle = πr²
Here, r = 1764
Therefore, the area of the circle = π × 1764² = 3.14 × 1764 × 1764 = 9,779,764.56 m².
Problem 4
The area of the square is 3,111,696 cm². Find the perimeter of the square.
The perimeter of the square is
Explanation
The area of the square = a²
Here, the area is 3,111,696 cm²
The length of the side is √3,111,696 = 1764
Perimeter of the square = 4a
Here, a = 1764
Therefore, the perimeter = 4 × 1764 = 7,056.
Problem 5
Find the square of 1800.
The square of 1800 is 3,240,000
Explanation
The square of 1800 is multiplying 1800 by 1800.
So, the square = 1800 × 1800 = 3,240,000
FAQs on Square of 1764
1.What is the square of 1764?
2.What is the square root of 1764?
3.Is 1764 a perfect square?
4.What are the first few multiples of 1764?
5.What is the square of 1700?
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 1764?
8.How do technology and digital tools in India support learning Algebra and Square of 1764?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for Square 1764.
- Perfect square: A number that is the square of an integer. For example, 1764 is a perfect square as it is 42².
- Exponential form: Exponential form is the way of writing a number in the form of a power. For example, 1764² where 1764 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: A number divisible by 2. For example, 1764 is an even number.
- Integer: A whole number that can be positive, negative, or zero. For example, -3, 0, and 42 are integers.
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Jaskaran Singh Saluja
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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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