Square Root of 873
2026-02-21 20:33 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-873

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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 873.

What is the Square Root of 873?

The square root is the inverse of the square of the number. 873 is not a perfect square. The square root of 873 is expressed in both radical and exponential form. In the radical form, it is expressed as √873, whereas (873)^(1/2) in the exponential form. √873 ≈ 29.542, 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 873

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where 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 873 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 873 is broken down into its prime factors:

Step 1: Finding the prime factors of 873

Breaking it down, we get 3 x 3 x 97: 3^2 x 97

Step 2: Now we found out the prime factors of 873. The second step is to make pairs of those prime factors. Since 873 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating √873 using prime factorization is not straightforward.

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Square Root of 873 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 873, we need to group it as 73 and 8.

Step 2: Now we need to find n whose square is 8. We can say n as ‘2’ because 2 x 2 is less than or equal to 8. Now the quotient is 2; after subtracting 4 from 8, the remainder is 4.

Step 3: Now let us bring down 73, which becomes the new dividend. Add the old divisor with the same number: 2 + 2, which gives us 4, our new divisor.

Step 4: Multiply the new divisor by a number m such that 4m x m ≤ 473. Let m be 7, then 47 x 7 = 329.

Step 5: Subtract 329 from 473; the difference is 144, and the quotient is 27.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 14400.

Step 7: Find a new divisor: 547. 547 x 2 = 1094

Step 8: Subtracting 1094 from 14400 gives us 13306.

Step 9: Continue doing these steps until we get two decimal places.

So the square root of √873 is approximately 29.54.

Square Root of 873 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 873 using the approximation method.

Step 1: Now we have to find the closest perfect squares to √873. The smallest perfect square less than 873 is 841, and the largest perfect square greater than 873 is 900. √873 falls somewhere between 29 and 30.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)

Using the formula: (873 - 841) / (900 - 841) = 0.542 The next step is adding the initial whole number to the decimal value, which is 29 + 0.542 = 29.542. Therefore, the square root of 873 is approximately 29.542.

Common Mistakes and How to Avoid Them in the Square Root of 873

Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in long division. Now let us look at a few mistakes students tend to make in detail.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √783?

Okay, lets begin

The area of the square is approximately 783 square units.

Explanation

The area of the square = side².

The side length is given as √783.

Area of the square = side² = √783 x √783 = 783.

Therefore, the area of the square box is approximately 783 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 873 square feet is built. If each of the sides is √873, what will be the square feet of half of the building?

Okay, lets begin

436.5 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 873 by 2 gives us 436.5.

So, half of the building measures 436.5 square feet.

Well explained 👍

Problem 3

Calculate √873 x 5.

Okay, lets begin

Approximately 147.71

Explanation

The first step is to find the square root of 873, which is approximately 29.54.

The second step is to multiply 29.54 by 5.

So, 29.54 x 5 ≈ 147.71.

Well explained 👍

Problem 4

What will be the square root of (873 + 27)?

Okay, lets begin

The square root is 30.

Explanation

To find the square root, we need to find the sum of (873 + 27). 873 + 27 = 900, and √900 = 30.

Therefore, the square root of (873 + 27) is ±30.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √783 units and the width ‘w’ is 38 units.

Okay, lets begin

The perimeter of the rectangle is approximately 118.08 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√783 + 38) = 2 × (27.97 + 38) ≈ 2 × 65.97 ≈ 131.94 units.

Well explained 👍

FAQ on Square Root of 873

1.What is √873 in its simplest form?

The prime factorization of 873 is 3 x 3 x 97, so the simplest form of √873 = √(3 x 3 x 97).

2.Mention the factors of 873.

Factors of 873 are 1, 3, 9, 97, 291, and 873.

3.Calculate the square of 873.

We get the square of 873 by multiplying the number by itself, that is 873 x 873 = 761,529.

4.Is 873 a prime number?

5.873 is divisible by?

873 has several factors; those are 1, 3, 9, 97, 291, and 873.

Important Glossaries for the Square Root of 873

  • Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, which 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, the positive square root is more commonly used due to its real-world applications. Hence, it is known as the principal square root.
     
  • Prime factorization: The process of expressing a number as the product of its prime factors.
     
  • Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.

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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.