Square Root of 872
2026-02-28 11:09 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-872

239 Learners

Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse of squaring a number is taking the square root. The square root concept is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 872.

What is the Square Root of 872?

The square root is the inverse operation of squaring a number. 872 is not a perfect square. The square root of 872 can be expressed in both radical and exponential forms. In radical form, it is expressed as √872, whereas in exponential form, it is expressed as (872)^(1/2). Calculating the approximate value, √872 ≈ 29.5305, which is an irrational number because it cannot be expressed in the form p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 872

For perfect square numbers, the prime factorization method is often used. However, for non-perfect square numbers like 872, methods such as the long-division method and approximation method are more suitable. Let us explore these methods: 

  • Prime factorization method 
  • Long division method 
  • Approximation method

Square Root of 872 by Prime Factorization Method

Prime factorization involves expressing a number as a product of prime factors. However, for non-perfect squares like 872, we cannot proceed with pairing prime factors. Let us look at how 872 is broken down into its prime factors.

Step 1: Finding the prime factors of 872

Breaking it down, we get 2 x 2 x 2 x 109: 2^3 x 109

Step 2: Since 872 is not a perfect square, the digits of the number cannot be grouped in pairs. Thus, calculating √872 using prime factorization directly is not feasible.

Explore Our Programs

Square Root of 872 by Long Division Method

The long division method is useful for finding the square root of non-perfect square numbers. Here's how you can find the square root using this method:

Step 1: Group the numbers from right to left in pairs. For 872, group as 87 and 2.

Step 2: Find a number whose square is ≤ 87. The number is 9 because 9^2 = 81 ≤ 87. The quotient becomes 9, and the remainder is 6 (87 - 81).

Step 3: Bring down the next pair, 2, making the new dividend 62.

Step 4: Double the quotient (9) to get 18, which will be part of the new divisor.

Step 5: Determine a digit, d, such that (180 + d) × d ≤ 620. The digit is 3, making the divisor 183.

Step 6: Multiply and subtract: 183 × 3 = 549, and 620 - 549 = 71.

Step 7: Add a decimal point and bring down pairs of zeros to continue the process until you reach the desired precision.

The square root of 872 using the long division method is approximately 29.5305.

Square Root of 872 by Approximation Method

The approximation method is another way to find the square root of a number. Here's how to find the square root of 872 using this method:

Step 1: Identify the closest perfect squares around 872. The smallest perfect square is 841 (29^2) and the largest is 900 (30^2). √872 is between 29 and 30.

Step 2: Use the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (872 - 841) / (900 - 841) = 31 / 59 ≈ 0.525

Step 3: Add this to the smaller square root: 29 + 0.525 = 29.525

So, the square root of 872 is approximately 29.525.

Common Mistakes and How to Avoid Them in the Square Root of 872

Students make mistakes such as forgetting about negative square roots and skipping steps in the long division method. Let us address a few common mistakes in detail.

Download Worksheets

Problem 1

Can you help Max find the area of a square box if its side length is given as √872?

Okay, lets begin

The area of the square is approximately 872 square units.

Explanation

The area of a square = side^2.

The side length is √872.

Area = (√872) × (√872) = 872

Therefore, the area of the square box is 872 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 872 square feet is built; if each of the sides is √872, what will be the square feet of half of the building?

Okay, lets begin

436 square feet

Explanation

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

Dividing 872 by 2 = 436

So, half of the building measures 436 square feet.

Well explained 👍

Problem 3

Calculate √872 × 5.

Okay, lets begin

Approximately 147.6525

Explanation

First, find the square root of 872, which is approximately 29.5305.

Then multiply by 5. 29.5305 × 5 ≈ 147.6525

Well explained 👍

Problem 4

What will be the square root of (800 + 72)?

Okay, lets begin

The square root is 30

Explanation

To find the square root, first calculate the sum: 800 + 72 = 872, and then calculate the square root. √872 ≈ 29.5305, but since the question specifies rounding, we use 30 for practical purposes.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √872 units and the width ‘w’ is 50 units.

Okay, lets begin

The perimeter of the rectangle is approximately 159.061 units.

Explanation

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

Perimeter = 2 × (√872 + 50) ≈ 2 × (29.5305 + 50) = 2 × 79.5305 = 159.061 units.

Well explained 👍

FAQ on Square Root of 872

1.What is √872 in its simplest form?

The prime factorization of 872 is 2 x 2 x 2 x 109, so the simplest form of √872 is √(2^3 x 109).

2.Mention the factors of 872.

Factors of 872 are 1, 2, 4, 8, 109, 218, 436, and 872.

3.Calculate the square of 872.

To find the square of 872, multiply the number by itself: 872 x 872 = 760,384.

4.Is 872 a prime number?

872 is not a prime number because it has more than two factors.

5.872 is divisible by?

872 is divisible by 1, 2, 4, 8, 109, 218, 436, and 872.

Important Glossaries for the Square Root of 872

  • Square root: The square root is the inverse of squaring a number. Example: 5^2 = 25, and the square root of 25 is √25 = 5.
     
  • Irrational number: An irrational number cannot be expressed as a simple fraction where both numerator and denominator are integers, with the denominator not being zero.
     
  • Long division method: A technique used to find the square root of non-perfect-square numbers through systematic division.
     
  • Radical expression: An expression that includes a root symbol, such as a square root or cube root.
     
  • Perfect square: A number that is the square of an integer. Example: 16 is a perfect square because 4^2 = 16.

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.