126 LearnersLast updated on May 26th, 2025
Square Root of 3796
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 3796.
What is the Square Root of 3796?
The square root is the inverse of the square of the number. 3796 is not a perfect square. The square root of 3796 is expressed in both radical and exponential form. In the radical form, it is expressed as √3796, whereas (3796)¹/² in the exponential form. √3796 ≈ 61.583, 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 3796
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 3796 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3796 is broken down into its prime factors.
Step 1: Finding the prime factors of 3796 Breaking it down, we get 2 x 2 x 13 x 73: 2² x 13¹ x 73¹
Step 2: Now we have found the prime factors of 3796. Since 3796 is not a perfect square, we cannot group all digits into pairs.
Therefore, calculating 3796 using prime factorization alone is not feasible.
Square Root of 3796 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 3796, we need to group it as 96 and 37.
Step 2: Now we need to find n whose square is close to 37. We can say n is 6 because 6 * 6 = 36, which is lesser than or equal to 37. Now the quotient is 6, and after subtracting 36 from 37, the remainder is 1.
Step 3: Now let us bring down 96, which makes the new dividend 196. Add the old divisor with the same number, 6 + 6, we get 12, which will be our new divisor.
Step 4: The new divisor is now 12n. We need to find the value of n such that 12n * n ≤ 196. Let us consider n as 1, now 12 * 1 * 1 = 12.
Step 5: Subtract 12 from 196; the difference is 184, and the quotient becomes 61.
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 zeros to the dividend. Now the new dividend is 18400.
Step 7: Now we need to find the new digit for the divisor, which is approximately 58, because 1218 * 1 = 1218.
Step 8: Subtracting 1218 from 18400 gives the result 17182.
Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue until the remainder is zero.
So the square root of √3796 ≈ 61.583.
Square Root of 3796 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 3796 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √3796. The smallest perfect square near 3796 is 3721 (which is 61²), and the largest perfect square is 3844 (which is 62²). √3796 falls somewhere between 61 and 62.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula, (3796 - 3721) / (3844 - 3721) = 75/123 ≈ 0.61. 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 61 + 0.61 = 61.61, so the square root of 3796 is approximately 61.61.
Common Mistakes and How to Avoid Them in the Square Root of 3796
Students do make mistakes while finding the square root, such as forgetting about the negative square root or 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; there is also -7.07, which should not be forgotten.
Mistake 2
Not adding square root symbols 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 before moving 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 ≈ 7.071067.
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 happen in subtraction or elsewhere.
Square Root of 3796 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3796?
The area of the square is approximately 3796 square units.
Explanation
The area of the square = side².
The side length is given as √3796.
Area of the square = side² = √3796 x √3796 = 3796.
Therefore, the area of the square box is 3796 square units.
Problem 2
A square-shaped building measuring 3796 square feet is built; if each of the sides is √3796, what will be the square feet of half of the building?
1898 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3796 by 2, we get 1898.
So half of the building measures 1898 square feet.
Problem 3
Calculate √3796 x 5.
Approximately 307.915
Explanation
The first step is to find the square root of 3796, which is approximately 61.583.
The second step is to multiply 61.583 with 5.
So 61.583 x 5 = 307.915.
Problem 4
What will be the square root of (3796 + 4)?
The square root is approximately 62.
Explanation
To find the square root, we need to find the sum of (3796 + 4).
3796 + 4 = 3800, and then 3800 ≈ 61.64.
Therefore, the square root of (3796 + 4) is approximately 61.64.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3796 units and the width ‘w’ is 20 units.
The perimeter of the rectangle is approximately 163.166 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3796 + 20)
= 2 × (61.583 + 20)
= 2 × 81.583
= 163.166 units.
FAQ on Square Root of 3796
1.What is √3796 in its simplest form?
2.Mention the factors of 3796.
3.Calculate the square of 3796.
4.Is 3796 a prime number?
5.3796 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 3796?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 3796?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 3796
- Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, which 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 the reason it is also known as a principal square root.
- Perfect square: A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it is 4².
- Approximation: Approximation is a method to find a value that is close to the exact value. For example, √3796 ≈ 61.583 is an approximation.
Explore More algebra
About BrightChamps in United States
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.
