102 LearnersLast updated on May 26th, 2025
Square Root of 881
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 881
What is the Square Root of 881?
The square root is the inverse of the square of the number. 881 is not a perfect square. The square root of 881 is expressed in both radical and exponential form. In the radical form, it is expressed as √881, whereas (881)^(1/2) in the exponential form. √881 ≈ 29.685, 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 881
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 881 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 881 is broken down into its prime factors:
Step 1: Finding the prime factors of 881
Breaking it down, we find that 881 = 7 × 7 × 13.
Step 2: Now we found out the prime factors of 881. The second step is to make pairs of those prime factors. Since 881 is not a perfect square, the digits of the number can’t be grouped in pairs such that all are used. Therefore, calculating √881 using prime factorization directly is not feasible for an exact value.
Square Root of 881 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 881, we need to group it as 81 and 8.
Step 2: Now, we need to find n whose square is less than or equal to 8. We can set n as 2 because 2 × 2 = 4, which is less than 8. The quotient is 2, and after subtracting 4 from 8, the remainder is 4.
Step 3: Now, bring down 81, making the new dividend 481. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor.
Step 4: The new divisor will be 4n. We need to find the largest n such that 4n × n ≤ 481. Let’s consider n as 9; then, 49 × 9 = 441.
Step 5: Subtract 441 from 481; the difference is 40, and the quotient is 29.
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 zeros to the dividend. Now the new dividend is 4000.
Step 7: Now, we need to find the new divisor that is 596 because 596 × 6 = 3576.
Step 8: Subtracting 3576 from 4000, we get the result 424.
Step 9: The quotient so far is 29.6. Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue till the remainder is zero.
So the square root of √881 is approximately 29.68.
Square Root of 881 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 881 using the approximation method.
Step 1: We have to find the closest perfect squares around √881. The smallest perfect square less than 881 is 841 (since 29² = 841) and the largest perfect square greater than 881 is 900 (since 30² = 900). √881 falls between 29 and 30.
Step 2: Now, apply the approximation formula: (Given number - Smaller perfect square) / (Larger perfect square - Smaller perfect square)
Using the formula (881 - 841) / (900 - 841) = 40 / 59 ≈ 0.68 Adding this to the smaller square root: 29 + 0.68 = 29.68, so the square root of 881 is approximately 29.68.
Common Mistakes and How to Avoid Them in the Square Root of 881
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 of those mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we typically consider only the positive square root, as it is often the required one in practical applications.
For example, the square root of 50 is 7.07, but there is also -7.07, which should not be forgotten.
Square Root of 881 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √881?
The area of the square is approximately 775.69 square units.
Explanation
The area of the square = side².
The side length is given as √881.
Area of the square = (√881)² = 29.685 × 29.685 ≈ 775.69.
Therefore, the area of the square box is approximately 775.69 square units.
Problem 2
A square-shaped building measuring 881 square feet is built; if each of the sides is √881, what will be the square feet of half of the building?
440.5 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 881 by 2 gives us 440.5.
So half of the building measures 440.5 square feet.
Problem 3
Calculate √881 × 5.
148.425
Explanation
The first step is to find the square root of 881, which is approximately 29.685.
The second step is to multiply 29.685 by 5.
So, 29.685 × 5 ≈ 148.425.
Problem 4
What will be the square root of (900 - 19)?
The square root is approximately 29.68.
Explanation
To find the square root, we need to find the difference of (900 - 19). 900 - 19 = 881, and √881 ≈ 29.68.
Therefore, the square root of (900 - 19) is approximately ±29.68.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √881 units and the width ‘w’ is 40 units.
The perimeter of the rectangle is approximately 139.37 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√881 + 40) ≈ 2 × (29.685 + 40) ≈ 2 × 69.685 ≈ 139.37 units.
FAQ on Square Root of 881
1.What is √881 in its simplest form?
2.Mention the factors of 881.
3.Calculate the square of 881.
4.Is 881 a prime number?
5.Is 881 divisible by any smaller numbers?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 881?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 881?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 881
- Square root: A square root is the inverse of a square. Example: 4² = 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 usually the positive square root that is used in real-world applications. This is known as the principal square root.
- Factors: Factors of a number are integers that can be multiplied to produce the original number.
- Decimal: If a number has a whole number and a fractional part, it is called a decimal. For example, 29.68, 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.
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