Last updated on May 26th, 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 11881.
The square root is the inverse of the square of the number. 11881 is a perfect square. The square root of 11881 is expressed in both radical and exponential form. In the radical form, it is expressed as √11881, whereas (11881)(1/2) in exponential form. √11881 = 109, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
The prime factorization method is often used for perfect square numbers. However, the long division method and approximation method can also be used. Let us now learn the following methods:
The product of prime factors is the prime factorization of a number. Now let us look at how 11881 is broken down into its prime factors.
Step 1: Finding the prime factors of 11881 Breaking it down, we get 11 x 11 x 11 x 11: 114
Step 2: Now we found out the prime factors of 11881. The second step is to make pairs of those prime factors. Since 11881 is a perfect square, we can pair the prime factors. Each pair of 11 contributes a factor of 11 to the square root. Thus, √11881 = 11 x 11 = 109.
The long division method is helpful for both perfect and non-perfect square numbers. Here, we will 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 11881, we group it as 11, 88, and 1.
Step 2: Now we need to find n whose square is less than or equal to 11. We can say n is 3 because 3 x 3 = 9, which is less than 11. Now the quotient is 3, and after subtracting 9 from 11, the remainder is 2.
Step 3: Bring down the next pair, which is 88, making the new dividend 288. Add the old divisor with the same number, 3 + 3, to get 6, which will be part of our new divisor.
Step 4: The new divisor is 6n. We need to find n such that 6n x n is less than or equal to 288. We find n is 4 because 64 x 4 = 256, which is less than 288.
Step 5: Subtract 256 from 288; the difference is 32. The next digit in the quotient is 4.
Step 6: Bring down the next pair, which is 1, making the new dividend 321. Add the old divisor with the last digit of the quotient, 64 + 4, to get 68, which will be part of our new divisor.
Step 7: The new divisor is 68n. We need to find n such that 68n x n is less than or equal to 321. We find n is 1 because 681 x 1 = 681, which is greater than 321.
Hence, n is 0, and the process has reached a conclusion with the quotient being 109. So the square root of √11881 is 109.
The approximation method is another approach to finding square roots. It is a simple method to find the square root of a given number. Let us learn how to find the square root of 11881 using the approximation method.
Step 1: Find the closest perfect square numbers around 11881. The closest perfect square numbers are 10816 (1042) and 12100 (1102). √11881 falls between 108 and 110.
Step 2: Since 11881 is exactly 1092, there is no need for further approximation. Therefore, the square root of 11881 is 109.
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping important steps in methods. Let's look at a few mistakes students tend to make in detail.
Can you help Max find the area of a square box if its side length is given as √11881?
The area of the square is 11881 square units.
The area of the square = side2.
The side length is given as √11881.
Area of the square = side2 = √11881 x √11881 = 109 x 109 = 11881.
Therefore, the area of the square box is 11881 square units.
A square-shaped building measuring 11881 square feet is built; if each of the sides is √11881, what will be the square feet of half of the building?
5940.5 square feet
We can divide the given area by 2 as the building is square-shaped.
Dividing 11881 by 2, we get 5940.5.
So half of the building measures 5940.5 square feet.
Calculate √11881 x 5.
545
The first step is to find the square root of 11881, which is 109.
The second step is to multiply 109 by 5.
So 109 x 5 = 545.
What will be the square root of (11881 + 19)?
The square root is approximately 109.091.
To find the square root, we need to find the sum of (11881 + 19). 11881 + 19 = 11900.
The square root of 11900 is approximately 109.091.
Find the perimeter of the rectangle if its length ‘l’ is √11881 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is 294 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√11881 + 38) = 2 × (109 + 38) = 2 × 147 = 294 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.