123 LearnersLast updated on May 26th, 2025
Square Root of 10368
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 10368.
What is the Square Root of 10368?
The square root is the inverse of the square of the number. 10368 is not a perfect square. The square root of 10368 is expressed in both radical and exponential form. In the radical form, it is expressed as √10368, whereas (10368)^(1/2) in the exponential form. √10368 ≈ 101.823376, 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 10368
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 10368 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 10368 is broken down into its prime factors.
Step 1: Finding the prime factors of 10368.
Breaking it down, we get 2^6 × 3^4: 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3.
Step 2: Now we found out the prime factors of 10368. The second step is to make pairs of those prime factors. Since 10368 is not a perfect square, therefore the digits of the number can’t be grouped into a complete pair. Therefore, calculating 10368 using prime factorization directly is not feasible.
Square Root of 10368 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 10368, we group it as 10 and 368.
Step 2: Now we need to find n whose square is close to 10. We can say n is ‘3’ because 3 x 3 = 9 is lesser than or equal to 10. Now the quotient is 3, after subtracting 9 from 10, the remainder is 1.
Step 3: Now let us bring down 368, which is the new dividend. Add the old divisor with the same number, 3 + 3, we get 6, which will be part of our new divisor.
Step 4: The new divisor will be in the form 6n. We need to find the value of n.
Step 5: The next step is finding 6n × n ≤ 1368. Let us consider n as 2, now 62 x 2 = 124.
Step 6: Subtract 124 from 1368, the difference is 144, and the quotient is 32.
Step 7: Since there are more digits left, bring them down and continue with the division process.
Step 8: Add a decimal point and continue the division until two decimal places are achieved.
So the square root of √10368 ≈ 101.82.
Square Root of 10368 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 10368 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √10368. The smallest perfect square less than 10368 is 10000, and the largest perfect square greater than 10368 is 10404. √10368 falls somewhere between 100 and 102.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (10368 - 10000) / (10404 - 10000) = 368 / 404 ≈ 0.91188.
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 100 + 0.91188 ≈ 100.91188, so the square root of 10368 is approximately 101.82.
Common Mistakes and How to Avoid Them in the Square Root of 10368
Students 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 has both positive and negative square roots. However, we typically take 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.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(12+24) ≠ √12 + √24, which is incorrect. The correct method is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 ≠ 7, the correct answer is √50 ≈ 7.071067.
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, as this will help them avoid mistakes.
For example: √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end. This may either happen in subtracting or elsewhere.
Square Root of 10368 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √10368?
The area of the square is 10368 square units.
Explanation
The area of the square = side^2.
The side length is given as √10368.
Area of the square = side^2 = √10368 × √10368 = 10368.
Therefore, the area of the square box is 10368 square units.
Problem 2
A square-shaped building measuring 10368 square feet is built; if each of the sides is √10368, what will be the square feet of half of the building?
5184 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 10368 by 2 = we get 5184.
So half of the building measures 5184 square feet.
Problem 3
Calculate √10368 × 5.
509.11688
Explanation
The first step is to find the square root of 10368, which is approximately 101.823376. The second step is to multiply 101.823376 by 5.
So, 101.823376 × 5 ≈ 509.11688.
Problem 4
What will be the square root of (10000 + 368)?
The square root is approximately 101.82
Explanation
To find the square root, we need to find the sum of (10000 + 368). 10000 + 368 = 10368, and then √10368 ≈ 101.82.
Therefore, the square root of (10000 + 368) is approximately 101.82.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √10368 units and the width ‘w’ is 100 units.
The perimeter of the rectangle is approximately 403.646752 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√10368 + 100) = 2 × (101.823376 + 100) = 2 × 201.823376 ≈ 403.646752 units.
FAQ on Square Root of 10368
1.What is √10368 in its simplest form?
2.Mention the factors of 10368.
3.Calculate the square of 10368.
4.Is 10368 a prime number?
5.10368 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 10368?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 10368?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 10368
- 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, so √16 = 4.
- Irrational number: An irrational number is a number that cannot be expressed as a simple fraction; it's non-repeating and non-terminating when written as a decimal.
- Principal square root: The principal square root is the non-negative square root of a number. Although a number has both positive and negative square roots, the principal square root is generally used.
- Decimal: A decimal is a number that is expressed in the base-10 numeral system, which consists of a whole number part and a fractional part separated by a decimal point.
- Long division method: A technique used to find the square root of a number by systematically dividing the number and finding its closest approximate root.
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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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