129 LearnersLast updated on May 29th, 2025
Square of 7225
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 7225.
What is the Square of 7225
The square of a number is the product of the number itself.
The square root of 7225 is the number that, when multiplied by itself, equals 7225.
We write it in math as √7225, where the square root symbol indicates the root value.
The square root of a positive number is always positive.
For example, √25=5; √36=6.
The square root of 7225 is √7225 = 85.
Square root of 7225 in exponential form: √7225
Square root of 7225 in arithmetic form: 85 × 85
How to Calculate the Value of the Square Root of 7225
The square root of a number is finding the number that, when multiplied by itself, gives the original number. Let’s learn how to find the square root of a number. These are the common methods used to find the square root of a number.
- By Prime Factorization Method
- Using a Calculator
By the Prime Factorization Method
In this method, we will find the prime factors of the number and pair them into two identical numbers. Let's find the square root of 7225.
Step 1: Identify the number. Here, the number is 7225
Step 2: Find the prime factors. The prime factorization of 7225 is 5 × 5 × 17 × 17.
Step 3: Pair the factors and find the square root. (5 × 17) × (5 × 17) = 85 × 85
The square root of 7225 is 85.
Using a Calculator
Using a calculator to find the square root of a number is the easiest method. Let’s learn how to use a calculator to find the square root of 7225.
Step 1: Enter the number in the calculator Enter 7225 in the calculator.
Step 2: Use the square root function (√) Press the square root button (√).
Step 3: Press the equal button to find the answer Here, the square root of 7225 is 85.
Tips and Tricks for the Square Root of 7225
Tips and tricks make it easy for students to understand and learn the square root of a number. To master the square root of a number, these tips and tricks will help students.
- The square root of an even number is a whole number only if the even number is a perfect square.
- The square root of an odd number is a whole number only if the odd number is a perfect square.
- If the square root of a number is a fraction or a decimal, then the number is not a perfect square. For example, √50 ≈ 7.07.
- The square root of a perfect square is always a whole number. For example, √144 = 12.
Common Mistakes to Avoid When Calculating the Square Root of 7225
Mistakes are common among students when doing math, especially when finding the square root of a number. Let’s learn some common mistakes to master square roots.
Mistake 1
Calculation errors:
Calculation errors mostly happen when students skip the steps or misinterpret the numbers. To avoid this, students should double-check the answer. They can double-check by squaring the solution they found.
For example, the square root of 64 is 8, and 8×8=64.
Mistake 2
Errors in using the formula.
The formula to find the square root of a number involves identifying its prime factors correctly. Students may confuse the process by incorrectly pairing factors. It's important to verify each step.
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 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 prime factorization.
Ignoring the correct prime factors when finding the square root of a number can lead to errors. So, students should thoroughly understand and correctly apply prime factorization.
Mistake 5
Not practicing regularly.
Regular practice is required to master the square root of a number. So students should engage in regular practice to avoid errors.
Solved Examples on Square Root of 7225
Problem 1
Find the length of each side of a square, where the area of the square is 7225 cm².
The area of a square = side² So, the area of a square = 7225 cm² So, the length of each side = √7225 = 85. The length of each side = 85 cm
Explanation
The length of a square is 85 cm.
Because the area is 7225 cm², the side length is √7225 = 85.
Problem 2
Anna is planning to tile her square floor with a side length of 85 feet. The cost to tile a square foot is 5 dollars. How much will it cost to tile the entire floor?
The side length of the floor = 85 feet The cost to tile 1 square foot of floor = 5 dollars. To find the total cost to tile, we find the area of the floor, Area of the floor = side² Here side = 85 Therefore, the area of the floor = 85 × 85 = 7225. The cost to tile the floor = 7225 × 5 = 36125. The total cost = 36125 dollars
Explanation
To find the cost to tile the floor, we multiply the area of the floor by the cost to tile per square foot.
So, the total cost is 36125 dollars.
Problem 3
Find the area of a circle whose radius is 85 meters.
The area of the circle = 22,698.84 m²
Explanation
The area of a circle = πr²
Here, r = 85
Therefore, the area of the circle = π × 85² = 3.14 × 85 × 85 = 22,698.84 m².
Problem 4
The area of a square is 7225 cm². Find the perimeter of the square.
The perimeter of the square is 340 cm.
Explanation
The area of the square = side²
Here, the area is 7225 cm²
The length of the side is √7225 = 85
Perimeter of the square = 4 × side
Here, side = 85
Therefore, the perimeter = 4 × 85 = 340 cm.
Problem 5
Find the square root of 7296.
The square root of 7296 is approximately 85.42.
Explanation
The square root of 7296 is found using a calculator or approximation methods.
So, the square root ≈ 85.42
FAQs on Square Root of 7225
1.What is the square root of 7225?
2.Is 7225 a perfect square?
3.What is a perfect square?
4.How do you find a square root without a calculator?
5.What are the first few prime factors of 7225?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square of 7225?
8.How do technology and digital tools in United States support learning Algebra and Square of 7225?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Square Root 7225.
- Perfect square: An integer that is the square of an integer. For example, 36 is a perfect square as it is 6².
- Prime factorization: Expressing a number as the product of its prime factors.
- Square root: The number that produces a specified quantity when multiplied by itself.
- Perimeter: The total length of the sides of a two-dimensional shape.
- Area: The measure of the surface enclosed within a set of lines.
Explore More algebra
![Important Math Links Icon]()
Previous to Square of 7225
About BrightChamps in United States
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.
