Square Root of 7321
2026-02-28 11:46 Diff
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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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 7321.

What is the Square Root of 7321?

The square root is the inverse of the square of a number. 7321 is not a perfect square. The square root of 7321 is expressed in both radical and exponential form: √7321 in radical form and (7321)^(1/2) in exponential form. √7321 ≈ 85.5561, 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 7321

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, 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 7321 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. However, since 7321 is not a perfect square, prime factorization is not suitable for finding its square root. Instead, the long division or approximation method is more appropriate.

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Square Root of 7321 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 7321, we start with 73 and 21.

Step 2: Now we need to find n whose square is less than or equal to 73. Here, n is 8 because 8 x 8 = 64, which is less than 73. The quotient is 8, and the remainder is 73 - 64 = 9.

Step 3: Bring down the next pair of digits, 21, making the new dividend 921.

Step 4: Double the quotient and write it with a blank space (16_), then find a digit to fill the blank that, when multiplied by the result, gives a product less than or equal to 921.

Step 5: Complete the division process, continuing to bring down pairs of zeros as necessary, to find more decimal places in the square root. Following this procedure, we find that √7321 ≈ 85.5561.

Square Root of 7321 by Approximation Method

The approximation method is another method for finding 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 7321 using the approximation method.

Step 1: Identify the closest perfect squares around 7321. The smallest perfect square less than 7321 is 7225, and the largest perfect square greater than 7321 is 7396. Thus, √7321 falls between 85 and 86.

Step 2: Use linear interpolation or estimation between these numbers to find a more exact value. Using this method, we approximate √7321 ≈ 85.5561.

Common Mistakes and How to Avoid Them in the Square Root of 7321

Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few common mistakes and how to avoid them.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √7321?

Okay, lets begin

The area of the square is approximately 53,612.3 square units.

Explanation

The area of a square is given by side². The side length is given as √7321. Area = (√7321)² = 7321. Therefore, the area of the square box is approximately 53,612.3 square units.

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Problem 2

A square-shaped building measuring 7321 square feet is built. If each of the sides is √7321, what will be the square feet of half of the building?

Okay, lets begin

3660.5 square feet

Explanation

To find half of the building's area, divide the total area by 2. 7321 ÷ 2 = 3660.5 So, half of the building measures 3660.5 square feet.

Well explained 👍

Problem 3

Calculate √7321 x 5.

Okay, lets begin

Approximately 427.7805

Explanation

First, find the square root of 7321, which is approximately 85.5561. Then multiply by 5: 85.5561 x 5 ≈ 427.7805

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Problem 4

What will be the square root of (7321 + 79)?

Okay, lets begin

The square root is approximately 86.0233

Explanation

To find the square root, first find the sum of (7321 + 79): 7321 + 79 = 7400. Then, √7400 ≈ 86.0233.

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Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √7321 units and the width ‘w’ is 50 units.

Okay, lets begin

The perimeter of the rectangle is approximately 271.1122 units.

Explanation

Perimeter of a rectangle = 2 × (length + width). Perimeter = 2 × (√7321 + 50) ≈ 2 × (85.5561 + 50) ≈ 271.1122 units.

Well explained 👍

FAQ on Square Root of 7321

1.What is √7321 in its simplest form?

Since 7321 is not a perfect square, its square root cannot be simplified into a simpler radical form. It is approximately √7321 = 85.5561.

2.Mention the factors of 7321.

The factors of 7321 are 1, 17, 431, and 7321.

3.Calculate the square of 7321.

The square of 7321 is found by multiplying the number by itself: 7321 x 7321 = 53,612,241.

4.Is 7321 a prime number?

7321 is not a prime number, as it has more than two factors.

5.What numbers is 7321 divisible by?

7321 is divisible by 1, 17, 431, and 7321.

Important Glossaries for the Square Root of 7321

  • Square root: A square root is the inverse operation of squaring a number. Example: 4² = 16, and the inverse square root is √16 = 4.
     
  • Irrational number: An irrational number cannot be expressed as a ratio of two integers. Its decimal form is non-repeating and non-terminating.
     
  • Long division method: A manual arithmetic technique to find the square root of numbers, particularly non-perfect squares, by a series of division steps.
     
  • Approximation method: A technique to estimate the square root of a number by identifying nearby perfect squares and interpolating between them
     
  • Factors: Numbers that divide another number exactly without leaving a remainder. For example, factors of 10 are 1, 2, 5, and 10.

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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.