128 LearnersLast updated on May 26th, 2025
Square Root of 10816
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.
What is 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.
Finding the Square Root of 10816
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:
- Prime factorization method
- Long division method
Square Root of 10816 by Prime Factorization Method
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.
Square Root of 10816 by Long Division Method
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.
Square Root of 10816 by Approximation Method
The approximation method is not typically necessary for perfect squares like 10816 since we can find the exact square root through other methods.
Common Mistakes and How to Avoid Them in the Square Root of 10816
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.
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 typically consider only the positive square root as it is the principal root.
For example: √10816 = 104, but there is also -104.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol properly is another mistake that students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before applying the square root.
For example: √(16) = 4, not 2 + 2.
Mistake 3
Not finding the correct value of a non-perfect square
Students might mistake the approximate value for the exact value.
For example, √50 is approximately 7.071, but students might incorrectly use 7 without considering the decimal.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly.
For example, √8 and ∛8 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, students might skip a step accidentally, resulting in a wrong answer.
Square Root of 10816 Examples
Problem 1
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.
Explanation
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.
Problem 2
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
Explanation
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.
Problem 3
Calculate √10816 x 5.
520
Explanation
The first step is to find the square root of 10816, which is 104, then multiply 104 by 5.
So 104 x 5 = 520.
Problem 4
What will be the square root of (10400 + 416)?
The square root is 104.
Explanation
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.
Problem 5
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.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√10816 + 38) = 2 × (104 + 38) = 2 × 142 = 284 units.
FAQ on Square Root of 10816
1.What is √10816 in its simplest form?
2.Mention the factors of 10816.
3.Calculate the square of 10816.
4.Is 10816 a prime number?
5.10816 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 10816?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 10816?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 10816
- Square root: A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root that is √16 = 4.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 9 is a perfect square because it is 3^2.
- Long division method: A method used to find the square root of a number by dividing it into pairs and successively finding digits of the quotient.
- Factorization: The process of breaking down a number into its prime factors.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
