115 LearnersLast updated on May 26th, 2025
Square Root of 3176
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 3176.
What is the Square Root of 3176?
The square root is the inverse of the square of the number. 3176 is not a perfect square. The square root of 3176 is expressed in both radical and exponential form. In the radical form, it is expressed as √3176, whereas (3176)^(1/2) in the exponential form. √3176 ≈ 56.355, 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 3176
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the 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 3176 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3176 is broken down into its prime factors.
Step 1: Finding the prime factors of 3176 Breaking it down, we get 2 x 2 x 2 x 397: 2^3 x 397
Step 2: Now we found out the prime factors of 3176. The second step is to make pairs of those prime factors. Since 3176 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 3176 using prime factorization is impossible.
Square Root of 3176 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 3176, we need to group it as 76 and 31.
Step 2: Now we need to find n whose square is 31. We can say n as ‘5’ because 5 x 5 = 25, which is less than or equal to 31. Now the quotient is 5, and after subtracting 31 - 25, the remainder is 6.
Step 3: Now let us bring down 76, which is the new dividend. Add the old divisor with the same number: 5 + 5 = 10, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 10n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 10n x n ≤ 676. Let us consider n as 6. Now 106 x 6 = 636.
Step 6: Subtract 676 from 636, and the difference is 40, and the quotient is 56.
Step 7: 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 8: Now we need to find the new divisor, which is 563.5, because 5635 x 5 = 28175.
Step 9: Subtracting 28175 from 40000, we get the result 11825.
Step 10: Now the quotient is 56.3.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue until the remainder is zero. So, the square root of √3176 is approximately 56.36.
Square Root of 3176 by Approximation Method
The approximation method is another method for finding square roots, and 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 3176 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √3176. The smallest perfect square close to 3176 is 3136, and the largest perfect square is 3249. √3176 falls somewhere between 56 and 57.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Going by the formula, (3176 - 3136) ÷ (3249 - 3136) = 40 ÷ 113 ≈ 0.354 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 56 + 0.354 = 56.354, so the square root of 3176 is approximately 56.354.
Common Mistakes and How to Avoid Them in the Square Root of 3176
Students do 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 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, and there is also -7.07, which should not be forgotten.
Mistake 2
Not adding the 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 a 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 ≈ 7.071.
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 subtraction or elsewhere.
Square Root of 3176 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3176?
The area of the square is approximately 3176 square units.
Explanation
The area of the square = side^2.
The side length is given as √3176.
Area of the square = side^2 = √3176 x √3176 = 3176.
Therefore, the area of the square box is approximately 3176 square units.
Problem 2
A square-shaped building measuring 3176 square feet is built; if each of the sides is √3176, what will be the square feet of half of the building?
1588 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3176 by 2, we get 1588.
So, half of the building measures 1588 square feet.
Problem 3
Calculate √3176 x 5.
Approximately 281.78
Explanation
The first step is to find the square root of 3176, which is approximately 56.36.
The second step is to multiply 56.36 by 5.
So, 56.36 x 5 ≈ 281.78.
Problem 4
What will be the square root of (3176 + 24)?
The square root is approximately 57.01.
Explanation
To find the square root, we need to find the sum of (3176 + 24).
3176 + 24 = 3200.
The square root of 3200 is approximately 57.01.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3176 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 212.72 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3176 + 50) ≈ 2 × (56.36 + 50) ≈ 2 × 106.36 ≈ 212.72 units.
FAQ on Square Root of 3176
1.What is √3176 in its simplest form?
2.Mention the factors of 3176.
3.Calculate the square of 3176.
4.Is 3176 a prime number?
5.3176 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 3176?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 3176?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 3176
- 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, it is always the positive square root that has more prominence due to its uses in the real world. That is why it is also known as the principal square root.
- Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors.
- Long division method: A method used to find the square root of non-perfect squares, involving repeated division and approximation.
Explore More algebra
About BrightChamps in Singapore
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.
