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 10816.
The square root is the inverse of the square of a number. 10816 is a perfect square. The square root of 10816 can be expressed in both radical and exponential form. In the radical form, it is expressed as √10816, whereas (10816)^(1/2) in the exponential form. √10816 = 104, 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 used for perfect square numbers. In the case of perfect squares, prime factorization can be an effective method to find the square root. 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 10816 is broken down into its prime factors:
Step 1: Finding the prime factors of 10816
Breaking it down, we get 2 x 2 x 2 x 2 x 13 x 13: 2^4 x 13^2
Step 2: Now we found out the prime factors of 10816. The second step is to make pairs of those prime factors. Since 10816 is a perfect square, the digits of the number can be grouped into pairs. Therefore, calculating √10816 using prime factorization is possible.
Step 3: From the pairs, we take one number from each pair: 2^2 x 13 = 4 x 13 = 52.
The long division method is particularly useful for perfect square numbers. 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 10816, we group it as 10 81 6.
Step 2: Now we need to find a number whose square is less than or equal to 10. We choose 3 because 3^2 = 9 is less than or equal to 10. Now the quotient is 3, and after subtracting 9 from 10, the remainder is 1.
Step 3: Bring down the next pair, 81, making the new dividend 181. Double the quotient (3) and write it next to 1, making it 6.
Step 4: Find the largest digit n such that 6n x n ≤ 181. We find n = 2 since 62 x 2 = 124 is less than 181.
Step 5: Subtract 124 from 181, resulting in 57. Bring down the next pair 16, making the new dividend 576.
Step 6: Double the quotient (32) to get 64, then find the largest digit n such that 64n x n ≤ 576. We find n = 9 since 649 x 9 = 576.
Step 7: Subtract 576 from 576, resulting in a remainder of 0, and the quotient is 104.
So the square root of √10816 is 104.
The approximation method is not typically necessary for perfect squares like 10816 since we can find the exact square root through other methods.
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in the methods. Now let us look at a few of those mistakes that students tend to make in detail.
Can you help Max find the area of a square box if its side length is given as √10816?
The area of the square is 10816 square units.
The area of the square = side^2.
The side length is given as √10816 = 104.
Area of the square = 104 x 104 = 10816.
Therefore, the area of the square box is 10816 square units.
A square-shaped building measuring 10816 square feet is built; if each of the sides is √10816, what will be the square feet of half of the building?
5408 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 10816 by 2 = we get 5408.
So half of the building measures 5408 square feet.
Calculate √10816 x 5.
520
The first step is to find the square root of 10816, which is 104, then multiply 104 by 5.
So 104 x 5 = 520.
What will be the square root of (10400 + 416)?
The square root is 104.
To find the square root, we need to find the sum of (10400 + 416). 10400 + 416 = 10816, and then √10816 = 104.
Therefore, the square root of (10400 + 416) is ±104.
Find the perimeter of the rectangle if its length ‘l’ is √10816 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 284 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√10816 + 38) = 2 × (104 + 38) = 2 × 142 = 284 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.