117 LearnersLast updated on May 26th, 2025
Square Root of 2156
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 2156.
What is the Square Root of 2156?
The square root is the inverse of the square of the number. 2156 is not a perfect square. The square root of 2156 is expressed in both radical and exponential form. In the radical form, it is expressed as √2156, whereas (2156)^(1/2) in the exponential form. √2156 ≈ 46.432, 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 2156
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 2156 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2156 is broken down into its prime factors.
Step 1: Finding the prime factors of 2156.
Breaking it down, we get 2 x 2 x 7 x 7 x 11: 2^2 x 7^2 x 11.
Step 2: Now we found out the prime factors of 2156. The second step is to make pairs of those prime factors. Since 2156 is not a perfect square, calculating 2156 using prime factorization directly is not straightforward.
Square Root of 2156 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 2156, we need to group it as 56 and 21.
Step 2: Now we need to find n whose square is less than or equal to 21. We can say n is '4' because 4 x 4 = 16, which is less than 21. Now the quotient is 4, and after subtracting 16 from 21, the remainder is 5.
Step 3: Now let us bring down 56, which is the new dividend. Add the old divisor with the same number 4 + 4 = 8, which will be our new divisor.
Step 4: We now have 8n as the new divisor. We need to find a digit n such that 8n x n ≤ 556. If n = 6, then 86 x 6 = 516.
Step 5: Subtract 516 from 556; the difference is 40.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4000.
Step 7: Now we need to find the new divisor, which is 927 because 927 x 4 = 3708.
Step 8: Subtracting 3708 from 4000, we get the result 292.
Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose there is no decimal value; continue till the remainder is zero.
So the square root of √2156 ≈ 46.43.
Square Root of 2156 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 2156 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √2156. The smallest perfect square less than 2156 is 2025 (45^2), and the largest perfect square greater than 2156 is 2209 (47^2). So, √2156 falls somewhere between 46 and 47.
Step 2: Now, apply the formula that is: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula: (2156 - 2025) / (2209 - 2025) = 131 / 184 ≈ 0.71. Add this to the base integer 46: 46 + 0.71 = 46.71. So the square root of 2156 is approximately 46.71.
Common Mistakes and How to Avoid Them in the Square Root of 2156
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 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 will be taking 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 is the wrong method of using roots. The right way of using roots 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 is wrong, 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 of the sum. This may either happen in subtracting or elsewhere.
Square Root of 2156 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2156?
The area of the square is approximately 2156 square units.
Explanation
The area of the square = side^2.
The side length is given as √2156.
Area of the square = side^2 = √2156 x √2156 = 2156.
Therefore, the area of the square box is approximately 2156 square units.
Problem 2
A square-shaped building measuring 2156 square feet is built; if each of the sides is √2156, what will be the square feet of half of the building?
1078 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2156 by 2, we get 1078.
So half of the building measures 1078 square feet.
Problem 3
Calculate √2156 x 5.
Approximately 232.16
Explanation
The first step is to find the square root of 2156, which is approximately 46.43.
The second step is to multiply 46.43 by 5.
So, 46.43 x 5 ≈ 232.16.
Problem 4
What will be the square root of (1156 + 1000)?
The square root is approximately 46.73.
Explanation
To find the square root, we need to find the sum of (1156 + 1000). 1156 + 1000 = 2156, and then √2156 ≈ 46.73.
Therefore, the square root of (1156 + 1000) is approximately ±46.73.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2156 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 169.86 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2156 + 38) = 2 × (46.43 + 38) = 2 × 84.43 ≈ 169.86 units.
FAQ on Square Root of 2156
1.What is √2156 in its simplest form?
2.Mention the factors of 2156.
3.Calculate the square of 2156.
4.Is 2156 a prime number?
5.2156 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 2156?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 2156?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 2156
- 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.
- 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 often more relevant in real-world applications. That is why it is also known as the principal square root.
- Perfect square: A perfect square is an integer that is the square of an integer. For example: 1, 4, 9, 16, 25 are perfect squares.
- Long Division Method: A method used to divide large numbers and find the square roots of non-perfect squares by determining successive approximations.
Explore More algebra
About BrightChamps in Qatar
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.
