125 LearnersLast updated on May 26th, 2025
Square Root of 872
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.
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.
Mistake 1
Forgetting about the negative square root
It's important to remember that numbers have both positive and negative square roots. However, in practical applications, we usually consider only the positive square root.
For example, √50 = ±7.071, but typically we use 7.071.
Mistake 2
Not adding the square root symbol in the proper places
Improper use of the square root symbol is a common error.
For example, √(12 + 24) ≠ √12 + √24. Instead, √(12 + 24) = √36 = 6.
Mistake 3
Not finding the correct value of a non-perfect square
Students should simplify numbers inside the square root to avoid errors.
For example, √50 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students should understand the difference between square roots and cube roots.
For instance, √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
The long division method involves multiple steps, and students might skip steps inadvertently, leading to incorrect answers. Ensure each step, especially subtraction and bringing down numbers, is performed correctly.
Square Root of 872 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √872?
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.
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?
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.
Problem 3
Calculate √872 × 5.
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
Problem 4
What will be the square root of (800 + 72)?
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.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √872 units and the width ‘w’ is 50 units.
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.
FAQ on Square Root of 872
1.What is √872 in its simplest form?
2.Mention the factors of 872.
3.Calculate the square of 872.
4.Is 872 a prime number?
5.872 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 872?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 872?
9.Does learning Algebra support future career opportunities for students in Singapore?
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.
Explore More algebra
About BrightChamps in Singapore
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.
