Square Root of 7200
2026-02-28 01:17 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-7200

330 Learners

Last updated on August 5, 2025

If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 7200.

What is the Square Root of 7200?

The square root is the inverse of the square of the number. 7200 is not a perfect square. The square root of 7200 is expressed in both radical and exponential form. In the radical form, it is expressed as √7200, whereas (7200)^(1/2) in the exponential form. √7200 ≈ 84.8528, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 7200

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method are used. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 7200 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 7200 is broken down into its prime factors.

Step 1: Finding the prime factors of 7200 Breaking it down, we get 2^4 × 3^2 × 5^2: 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

Step 2: Now we found the prime factors of 7200. The second step is to make pairs of those prime factors. Since 7200 is not a perfect square, therefore the digits of the number can’t be grouped in complete pairs. Therefore, calculating 7200 using prime factorization results in √7200 = 2^2 × 3 × 5 × √2 = 60√2 ≈ 84.8528.

Explore Our Programs

Square Root of 7200 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 7200, we need to group it as 00 and 72.

Step 2: Now we need to find n whose square is closest to 72. We can say n is '8' because 8 × 8 = 64 is less than 72. Now the quotient is 8, subtracting 64 from 72 gives a remainder of 8.

Step 3: Bring down 00, making the new dividend 800.

Step 4: Double the quotient, which is 8, to get 16. This will be part of our new divisor, which will be 16n.

Step 5: Find a digit n such that 16n × n is less than or equal to 800. Let n be 4, then 164 × 4 = 656.

Step 6: Subtract 656 from 800, the remainder is 144, and add decimal point to quotient, making it 84.

Step 7: Bring down the next pair of zeros, making the new dividend 14400.

Step 8: Double the quotient (84), making it 168, and find a digit n such that 168n × n is less than or equal to 14400. Let n be 8, then 1688 × 8 = 13504.

Step 9: Subtract 13504 from 14400, the remainder is 896.

Step 10: Continue doing these steps until you get the desired number of decimal places. So, the approximate square root of √7200 is 84.8528.

Square Root of 7200 by Approximation Method

Approximation method is another method for finding the square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 7200 using the approximation method.

Step 1: Now we have to find the closest perfect square of √7200. The smallest perfect square less than 7200 is 7056, and the largest perfect square greater than 7200 is 7225. √7200 falls somewhere between 84 and 85.

Step 2: Apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Using the formula (7200 - 7056) ÷ (7225 - 7056) ≈ 0.8528. Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 84 + 0.8528 = 84.8528. So, the square root of 7200 is approximately 84.8528.

Common Mistakes and How to Avoid Them in the Square Root of 7200

Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √7200?

Okay, lets begin

The area of the square is 7200 square units.

Explanation

The area of the square = side^2. The side length is given as √7200. Area of the square = side^2 = √7200 × √7200 = 7200. Therefore, the area of the square box is 7200 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 7200 square feet is built; if each of the sides is √7200, what will be the square feet of half of the building?

Okay, lets begin

3600 square feet

Explanation

We can just divide the given area by 2, as the building is square-shaped. Dividing 7200 by 2 = we get 3600. So, half of the building measures 3600 square feet.

Well explained 👍

Problem 3

Calculate √7200 × 5.

Okay, lets begin

424.264

Explanation

The first step is to find the square root of 7200, which is approximately 84.8528. The second step is to multiply 84.8528 by 5. So, 84.8528 × 5 ≈ 424.264.

Well explained 👍

Problem 4

What will be the square root of (7200 + 25)?

Okay, lets begin

The square root is 85.

Explanation

To find the square root, we need to find the sum of (7200 + 25). 7200 + 25 = 7225, and then √7225 = 85. Therefore, the square root of (7200 + 25) is ±85.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √7200 units and the width ‘w’ is 50 units.

Okay, lets begin

We find the perimeter of the rectangle as 269.7056 units.

Explanation

Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√7200 + 50) = 2 × (84.8528 + 50) ≈ 2 × 134.8528 = 269.7056 units.

Well explained 👍

FAQ on Square Root of 7200

1.What is √7200 in its simplest form?

The prime factorization of 7200 is 2^4 × 3^2 × 5^2, so the simplest form of √7200 = √(2^4 × 3^2 × 5^2) = 60√2.

2.Mention the factors of 7200.

Factors of 7200 include 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 2400, 3600, and 7200.

3.Calculate the square of 7200.

We get the square of 7200 by multiplying the number by itself, which is 7200 × 7200 = 51840000.

4.Is 7200 a prime number?

7200 is not a prime number, as it has more than two factors.

5.7200 is divisible by?

7200 has many factors; it is divisible by numbers such as 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 2400, 3600, and 7200.

Important Glossaries for the Square Root of 7200

  • Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.
     
  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
     
  • Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
     
  • Prime factorization: Breaking down a number into its basic building blocks, which are prime numbers. For example, the prime factorization of 7200 is 2^4 × 3^2 × 5^2.
     
  • Decimal approximation: A method to estimate the value of a square root to a certain number of decimal places for practical use. For example, √7200 ≈ 84.8528.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.