126 LearnersLast updated on May 26th, 2025
Square Root of 13456
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 various fields such as architecture, finance, and engineering. Here, we will discuss the square root of 13456.
What is the Square Root of 13456?
The square root is the inverse of the square of a number. 13456 is not a perfect square. The square root of 13456 is expressed in both radical and exponential form. In radical form, it is expressed as √13456, whereas in exponential form it is expressed as (13456)(1/2). √13456 ≈ 116.007, 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 13456
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not 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 13456 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 13456 is broken down into its prime factors.
Step 1: Finding the prime factors of 13456 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 421: 25 x 421
Step 2: Now we found out the prime factors of 13456. The second step is to make pairs of those prime factors. Since 13456 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 13456 using prime factorization to find its square root is not feasible.
Square Root of 13456 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 13456, we need to group it as 56, 34, and 1.
Step 2: Now we need to find n whose square is less than or equal to 13. We can say n is '3' because 3 x 3 = 9, which is less than 13. Now the quotient is 3, and after subtracting 9 from 13, the remainder is 4.
Step 3: Bring down 34 to make the new dividend 434. Add the old divisor (3) to itself to get 6, which will be the start of our new divisor.
Step 4: Now we need to find n such that 6n x n ≤ 434. Let n be 7, then 67 x 7 = 469, which is greater than 434, so n should be 6.
Step 5: Subtract 396 from 434, leaving a remainder of 38. Now the quotient is 36. Step 6: Bring down 56 to make the new dividend 3856.
Step 7: The new divisor starts with 72. Repeat the process until two decimal places are achieved. The square root of 13456 is approximately 116.007.
Square Root of 13456 by Approximation Method
The approximation method is another method for finding square roots. It is an easy way to find the square root of a given number. Now let us learn how to find the square root of 13456 using the approximation method.
Step 1: Now we have to find the closest perfect square numbers to √13456. The closest perfect squares are 13456 and 14400. √13456 falls between 116 and 120.
Step 2: Now we need to apply the formula (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Applying the formula: (13456 - 13456) / (14400 - 13456) = 0 Using the formula, the square root approximation is 116.
Common Mistakes and How to Avoid Them in the Square Root of 13456
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important for students to understand that a number has both positive and negative square roots. However, we typically use only the positive square root in real-world applications. For example, √50 = 7.07; there is also -7.07, which should not be forgotten.
Square root of 13456 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √134?
The area of the square is 134 square units.
Explanation
The area of the square = side2.
The side length is given as √134.
Area of the square = (√134) x (√134) = 134.
Therefore, the area of the square box is 134 square units.
Problem 2
A square-shaped building measuring 13456 square feet is built; if each of the sides is √13456, what will be the square feet of half of the building?
6728 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 13456 by 2 = we get 6728.
So half of the building measures 6728 square feet.
Problem 3
Calculate √13456 x 5.
580.035
Explanation
The first step is to find the square root of 13456, which is approximately 116.007.
The second step is to multiply 116.007 by 5.
So 116.007 x 5 = 580.035.
Problem 4
What will be the square root of (134 + 6)?
The square root is 12.
Explanation
To find the square root, we need to find the sum of (134 + 6). 134 + 6 = 140, and then √140 ≈ 11.83.
Therefore, the approximate square root of (134 + 6) is ±11.83.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √134 units and the width ‘w’ is 34 units.
We find the perimeter of the rectangle as 95.66 units.
Explanation
Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√134 + 34) ≈ 2 × (11.57 + 34) = 2 × 45.57 = 91.14 units.
FAQ on Square Root of 13456
1.What is √13456 in its simplest form?
2.Mention the factors of 13456.
3.Calculate the square of 13456.
4.Is 13456 a prime number?
5.13456 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 13456?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 13456?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 13456
- Square root: A square root is the inverse of a square. Example: 42 = 16, and the inverse of the square is the square root, that is, √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots; however, the positive square root is more commonly used due to its practical applications.
- Prime factorization: This is the process of expressing a number as the product of its prime factors.
- Long division method: A technique used to find the square root of non-perfect squares through iterative division and subtraction.
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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.
