117 LearnersLast updated on May 27th, 2025
Square of 4225
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 4225.
What is the Square of 4225
The square of a number is the product of the number with itself.
The square of 4225 is 65 × 65.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 65², where 65 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 65 is 65 × 65 = 4225.
Square of 65 in exponential form: 65²
Square of 65 in arithmetic form: 65 × 65
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How to Calculate the Value of Square of 4225
The square of a number is found by multiplying the number by itself. 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 65.
Step 1: Identify the number. Here, the number is 65.
Step 2: Multiplying the number by itself, we get, 65 × 65 = 4225.
The square of 65 is 4225.
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 into the equation.
Here, ‘a’ is 65. So: 65² = 65 × 65 = 4225
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 65.
Step 1: Enter the number in the calculator Enter 65 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is 65 × 65
Step 3: Press the equal to button to find the answer Here, the square of 65 is 4225.
Tips and Tricks for the Square of 4225
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 4225
Mistakes are common among kids when doing math, especially when it involves 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 steps or swap the digits. To avoid this, students should double-check their answers. 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 652 as (6 + 5)² or (60 + 5)². Students should check and use the correct formula and double-check their answers to avoid 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 this, 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. Students should understand parentheses and perform operations in the correct order to avoid error.
Mistake 5
Not practicing regularly.
Regular practice is required to master the square of a number. Students should do regular practice to avoid errors.
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Solved Examples on Square of 4225
Problem 1
Find the side length of a square whose area is 4225 cm².
The area of a square = a²
So, the area of a square = 4225 cm²
So, the side length = √4225 = 65.
The length of each side = 65 cm
Explanation
The length of a square is 65 cm because the area is 4225 cm², so the length is √4225 = 65.
Problem 2
Sarah wants to tile her square floor of side 65 feet. The cost to tile one square foot is 4 dollars. How much will it cost to tile the entire floor?
The side length of the floor = 65 feet
The cost to tile 1 square foot of floor = 4 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 = 65
Therefore, the area of the floor = 65² = 65 × 65 = 4225.
The cost to tile the floor = 4225 × 4 = 16900.
The total cost = 16900 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 16900 dollars.
Problem 3
Find the area of a circle whose radius is 65 meters.
The area of the circle = 13,273.39 m²
Explanation
The area of a circle = πr²
Here, r = 65
Therefore, the area of the circle = π × 65² = 3.14 × 65 × 65 = 13,273.39 m².
Problem 4
The area of a square is 4225 cm². Find the perimeter of the square.
The perimeter of the square is 260 cm.
Explanation
The area of the square = a²
Here, the area is 4225 cm²
The side length is √4225 = 65
Perimeter of the square = 4a
Here, a = 65
Therefore, the perimeter = 4 × 65 = 260.
Problem 5
Find the square of 66.
The square of 66 is 4356.
Explanation
The square of 66 is found by multiplying 66 by 66.
So, the square = 66 × 66 = 4356.
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FAQs on Square of 4225
1.What is the square of 65?
2.What is the square root of 4225?
3.Is 65 a prime number?
4.What are the first few multiples of 65?
5.What is the square of 64?
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Important Glossaries for Square of 4225.
- Perfect square: A number that is the square of an integer. For example, 36 is a perfect square because it is 6².
- Square root: The number that, when multiplied by itself, gives the original number. For example, the square root of 64 is 8.
- Even number: A number that is divisible by 2 with no remainder. For example, 4, 6, 8, etc.
- Odd number: A number that is not divisible by 2. For example, 3, 5, 7, etc.
- Multiplication: The arithmetic operation of combining numbers to find their total equivalent value. For example, 4 multiplied by 3 equals 12.
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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.
