133 LearnersLast updated on May 29th, 2025
Square of 707
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 707.
What is the Square of 707
The square of a number is the product of the number itself.
The square of 707 is 707 × 707.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 707², where 707 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 707 is 707 × 707 = 499,849.
Square of 707 in exponential form: 707²
Square of 707 in arithmetic form: 707 × 707
How to Calculate the Value of the Square of 707
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 707.
Step 1: Identify the number. Here, the number is 707.
Step 2: Multiplying the number by itself, we get, 707 × 707 = 499,849.
The square of 707 is 499,849.
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 707
So: 707² = 707 × 707 = 499,849
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 707.
Step 1: Enter the number in the calculator. Enter 707 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 707 × 707
Step 3: Press the equal to button to find the answer. Here, the square of 707 is 499,849.
Tips and Tricks for the Square of 707
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 707
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 707² with (7 + 0 + 7)² or (700 + 7)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 707
Problem 1
Find the length of the square, where the area of the square is 499,849 cm².
The area of a square = a²
So, the area of a square = 499,849 cm²
So, the length = √499,849 = 707.
The length of each side = 707 cm
Explanation
The length of a square is 707 cm.
Because the area is 499,849 cm², the length is √499,849 = 707.
Problem 2
A farmer is planning to fence his square field of length 707 meters. The cost to fence a meter is 5 dollars. Then how much will it cost to fence the entire field?
The length of the field = 707 meters
The cost to fence 1 meter of the field = 5 dollars.
To find the total cost to fence, we find the perimeter of the field.
Perimeter of the field = 4 × 707 = 2828 meters.
The cost to fence the field = 2828 × 5 = 14,140.
The total cost = 14,140 dollars
Explanation
To find the cost to fence the field, we multiply the perimeter of the field by the cost to fence per meter. So, the total cost is 14,140 dollars.
Problem 3
Find the area of a circle whose radius is 707 meters.
The area of the circle = 1,569,287.46 m²
Explanation
The area of a circle = πr²
Here, r = 707
Therefore, the area of the circle = π × 707² = 3.14 × 707 × 707 = 1,569,287.46 m².
Problem 4
The area of a square is 500,000 cm². Find the approximate length of the side of the square.
The approximate length of the side of the square is 707 cm.
Explanation
The area of the square = a² Here, the area is 500,000 cm².
So, the length of the side is approximately √500,000 ≈ 707.
Problem 5
Find the square of 708.
The square of 708 is 501,264.
Explanation
The square of 708 is multiplying 708 by 708.
So, the square = 708 × 708 = 501,264.
FAQs on Square of 707
1.What is the square of 707?
2.What is the square root of 707?
3.Is 707 a prime number?
4.What are the first few multiples of 707?
5.What is the square of 706?
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 707?
8.How do technology and digital tools in India support learning Algebra and Square of 707?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for Square of 707.
- Perfect square: A number that is the square of an integer. For example, 1, 4, 9, 16, 25, etc.
- Exponent: The power to which a number is raised. It indicates how many times the number is multiplied by itself. For example, in 707², 2 is the exponent.
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number.
- Multiplication method: A method to find the square by multiplying the number by itself.
- Formula: A mathematical expression used to calculate a value. For example, a² is the formula to calculate the square of a number a.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
