103 LearnersLast updated on May 26th, 2025
Square Root of 10376
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 10376
What is the Square Root of 10376?
The square root is the inverse of the square of a number. 10376 is a perfect square. The square root of 10376 is expressed in both radical and exponential form. In radical form, it is expressed as √10376, whereas in exponential form it is expressed as (10376)^(1/2). √10376 = 102, 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 10376
The prime factorization method is used for perfect square numbers. For non-perfect square numbers, methods like long division and approximation are used. Let us now learn the method for 10376:
- Prime factorization method
Square Root of 10376 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 10376 is broken down into its prime factors:
Step 1: Finding the prime factors of 10376 Breaking it down, we get 2 x 2 x 2 x 2 x 11 x 11 x 11: 2^4 x 11^2
Step 2: Now we found out the prime factors of 10376. The next step is to make pairs of those prime factors. Since 10376 is a perfect square, we can pair all the factors.
Step 3: Taking one factor from each pair, we get 2^2 x 11 = 102.
So, the square root of 10376 using prime factorization is 102.
Square Root of 10376 by Long Division Method
The long division method is used for both perfect and non-perfect square numbers. Let's find the square root using the long division method, step by step:
Step 1: Pair the digits of 10376 starting from the right. So, we have pairs: 10 and 376.
Step 2: Find the largest number whose square is less than or equal to 10. In this case, it is 3, since 3 x 3 = 9.
Step 3: Subtract 9 from 10, giving a remainder of 1. Bring down the next pair, 376, making it 1376.
Step 4: Double the divisor (3) to get 6, and determine a new digit, n, such that 6n x n is less than or equal to 1376. The number n is 2, since 62 x 2 = 124.
Step 5: Subtract 124 from 1376 to get the remainder 12.
Step 6: Bring down the next pair of zeroes, making it 1200. Double the divisor (32) and find the next digit, which is 0, since 640 x 0 = 0.
Step 7: Continue the process until the remainder is zero.
Finally, the square root of 10376 is 102.
Square Root of 10376 by Approximation Method
The approximation method is used for estimating the square roots of numbers. However, since 10376 is a perfect square, this method is not necessary. We have already established that √10376 = 102.
Common Mistakes and How to Avoid Them in the Square Root of 10376
Students can make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in methods. Let's explore some common 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, the principal square root is usually the positive one used in real-world applications.
For example, √10376 = 102, but there is also -102.
Square root of 10376 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √10376?
The area of the square is 107,584 square units.
Explanation
The area of the square = side^2.
The side length is given as √10376.
Area of the square = side^2 = √10376 x √10376 = 102 x 102 = 107,584
Therefore, the area of the square box is 107,584 square units.
Problem 2
A square-shaped building measuring 10376 square feet is built; if each of the sides is √10376, what will be the square feet of half of the building?
5,188 square feet
Explanation
Since the building is square-shaped, we simply divide the total area by 2.
Dividing 10376 by 2, we get 5,188.
So, half of the building measures 5,188 square feet.
Problem 3
Calculate √10376 x 5.
510
Explanation
The first step is to find the square root of 10376, which is 102.
The second step is to multiply 102 by 5.
So, 102 x 5 = 510
Problem 4
What will be the square root of (10368 + 8)?
The square root is 102
Explanation
To find the square root, find the sum of (10368 + 8). 10368 + 8 = 10376, and then √10376 = 102.
Therefore, the square root of (10368 + 8) is ±102.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √10376 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is 280 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√10376 + 38) = 2 × (102 + 38) = 2 × 140 = 280 units.
FAQ on Square Root of 10376
1.What is √10376 in its simplest form?
2.Mention the factors of 10376.
3.Calculate the square of 10376.
4.Is 10376 a prime number?
5.10376 is divisible by?
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 10376?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 10376?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 10376
Square root: The 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.
Perfect square: A number that can be expressed as the product of an integer with itself. Example: 144 is a perfect square because it is 12 x 12.
Rational number: A rational number can be expressed in the form of p/q, where p and q are integers and q is not equal to zero.
Principal square root: The positive square root of a number, which is commonly used in real-world applications.
Factorization: Breaking down a number into its prime components. Example: The prime factorization of 18 is 2 x 3^2.
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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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