102 LearnersLast updated on May 26th, 2025
Square Root of 1331
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 1331.
What is the Square Root of 1331?
The square root is the inverse of the square of the number. 1331 is not a perfect square, but it has a cube root which is an integer. The square root of 1331 is expressed in both radical and exponential form. In radical form, it is expressed as √1331, whereas (1331)^(1/2) in exponential form. The square root of 1331 is approximately 36.4692, 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 1331
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not typically 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 1331 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1331 is broken down into its prime factors.
Step 1: Finding the prime factors of 1331
Breaking it down, we get 11 x 11 x 11: 11^3
Step 2: Now we found out the prime factors of 1331. Since 1331 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 1331 using prime factorization for its square root is not straightforward because it is not a perfect square.
Square Root of 1331 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 1331, we need to group it as 31 and 13.
Step 2: Now we need to find n whose square is less than or equal to 13. We can say n as ‘3’ because 3^2 is 9 which is lesser than or equal to 13. Now the quotient is 3 after subtracting 13-9 the remainder is 4.
Step 3: Now let us bring down 31 which is the new dividend. Add the old divisor with the same number 3 + 3 to get 6 which will be our new divisor.
Step 4: We need to find a digit n such that 6n × n is less than or equal to 431. In this case, n is 7 since 67 × 7 = 469 which is too large, but 66 × 6 = 396 is less than 431.
Step 5: Subtract 396 from 431 to get 35, and the quotient is now 36.
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 3500.
Step 7: Continue this process to find the decimal values.
So the square root of √1331 is approximately 36.4692.
Square Root of 1331 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 1331 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1331. The closest perfect squares around 1331 are 1296 and 1369. √1331 falls somewhere between 36 and 37.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1331 - 1296) ÷ (1369 - 1296) = 35/73 ≈ 0.4795. Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 36 + 0.4795 ≈ 36.4795, so the square root of 1331 is approximately 36.4795.
Common Mistakes and How to Avoid Them in the Square Root of 1331
Students do make mistakes while finding the square root, such as forgetting about the negative square root. Skipping long division methods etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √50 = 7.07, there is also -7.07 which should not be forgotten.
Square Root of 1331 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1331?
The area of the square is approximately 1331 square units.
Explanation
The area of the square = side².
The side length is given as √1331.
Area of the square = side² = √1331 × √1331 = 1331.
Therefore, the area of the square box is 1331 square units.
Problem 2
A square-shaped building measuring 1331 square feet is built; if each of the sides is √1331, what will be the square feet of half of the building?
665.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1331 by 2 = we get 665.5.
So half of the building measures 665.5 square feet.
Problem 3
Calculate √1331 × 5.
Approximately 182.345
Explanation
The first step is to find the square root of 1331 which is approximately 36.4692, the second step is to multiply 36.4692 with 5.
So 36.4692 × 5 ≈ 182.345.
Problem 4
What will be the square root of (1300 + 31)?
The square root is approximately 36.4692.
Explanation
To find the square root, we need to find the sum of (1300 + 31). 1300 + 31 = 1331, and then √1331 ≈ 36.4692.
Therefore, the square root of (1300 + 31) is approximately ±36.4692.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1331 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 148.94 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1331 + 38) = 2 × (36.4692 + 38) = 2 × 74.4692 ≈ 148.94 units.
FAQ on Square Root of 1331
1.What is √1331 in its simplest form?
2.Mention the factors of 1331.
3.Calculate the square of 1331.
4.Is 1331 a prime number?
5.1331 is divisible by?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 1331?
8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 1331?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for the Square Root of 1331
- 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, 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 always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
- Prime factorization: Prime factorization is the process of expressing a number as the product of its prime numbers. For example, the prime factorization of 18 is 2 × 3².
- Long division method: The long division method is a technique used to find the square root of a number by dividing it into smaller parts.
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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
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