137 LearnersLast updated on May 26th, 2025
Square Root of 3136
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 3136.
What is the Square Root of 3136?
The square root is the inverse of the square of the number. 3136 is a perfect square. The square root of 3136 is expressed in both radical and exponential form. In the radical form, it is expressed as √3136, whereas (3136)^(1/2) in the exponential form. √3136 = 56, 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 3136
The prime factorization method can be used for perfect square numbers. For non-perfect square numbers, methods like long-division and approximation are used. Let us now learn the following methods for finding the square root of 3136:
- Prime factorization method
- Long division method
Square Root of 3136 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3136 is broken down into its prime factors.
Step 1: Finding the prime factors of 3136 Breaking it down, we get 2 x 2 x 2 x 2 x 7 x 7: 2^4 x 7^2
Step 2: Now we found the prime factors of 3136. The second step is to make pairs of those prime factors. Since 3136 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating 3136 using prime factorization is possible.
Step 3: Taking one number from each pair gives us 2^2 x 7 = 4 x 7 = 28 Thus, the square root of 3136 is 56.
Square Root of 3136 by Long Division Method
The long division method is used to find the square root of perfect square numbers too. 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 3136, we need to group it as 36 and 31.
Step 2: Now we need to find n whose square is less than or equal to 31. We can say n as '5' because 5^2 = 25 is less than 31. Now the quotient is 5; after subtracting 25 from 31, the remainder is 6.
Step 3: Now let us bring down 36, 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 10n. We need to find the value of n such that 10n x n ≤ 636. Let's consider n as 6; now 106 x 6 = 636.
Step 5: Subtract 636 from 636; the difference is 0, and the quotient is 56. So the square root of √3136 is 56.
Square Root of 3136 by Approximation Method
The approximation method is not necessary for perfect squares but can be applied to understand the proximity of results. For 3136, direct methods are more efficient.
Common Mistakes and How to Avoid Them in the Square Root of 3136
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. 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 generally take only the positive square root, as it is the required one.
For example, √3136 = 56, but there is also -56, 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 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 keep away from 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 3136 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3136?
The area of the square is 3136 square units.
Explanation
The area of the square = side^2.
The side length is given as √3136.
Area of the square = side^2 = √3136 x √3136 = 56 x 56 = 3136.
Therefore, the area of the square box is 3136 square units.
Problem 2
A square-shaped building measuring 3136 square feet is built; if each of the sides is √3136, what will be the square feet of half of the building?
1568 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3136 by 2, we get 1568.
So half of the building measures 1568 square feet.
Problem 3
Calculate √3136 x 5.
280
Explanation
The first step is to find the square root of 3136, which is 56.
The second step is to multiply 56 by 5.
So 56 x 5 = 280.
Problem 4
What will be the square root of (3130 + 6)?
The square root is 56.
Explanation
To find the square root, we need to find the sum of (3130 + 6).
3130 + 6 = 3136, and then √3136 = 56.
Therefore, the square root of (3130 + 6) is ±56.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √3136 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is 188 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3136 + 38) = 2 × (56 + 38) = 2 × 94 = 188 units.
FAQ on Square Root of 3136
1.What is √3136 in its simplest form?
2.Mention the factors of 3136.
3.Calculate the square of 3136.
4.Is 3136 a prime number?
5.3136 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 3136?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 3136?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 3136
- Square root: A square root is the inverse of a square. For example, 7^2 = 49, and the inverse of the square is the square root, that is, √49 = 7.
- Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 36 is a perfect square because it is 6^2.
- Prime factorization: Prime factorization is expressing a number as the product of its prime factors.
- Divisor: A divisor is a number that divides another number completely without leaving a remainder. For instance, 7 is a divisor of 49.
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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.
