101 LearnersLast updated on May 26th, 2025
Square Root of 3722.1835
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 engineering, finance, etc. Here, we will discuss the square root of 3722.1835.
What is the Square Root of 3722.1835?
The square root is the inverse operation of squaring a number. 3722.1835 is not a perfect square. The square root of 3722.1835 can be expressed in both radical and exponential form. In radical form, it is expressed as √3722.1835, whereas in exponential form it is (3722.1835)^(1/2). The approximate value of √3722.1835 is 61.0113, which is an irrational number because it cannot be expressed as a fraction of two integers.
Finding the Square Root of 3722.1835
The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers, we often use the long-division method and approximation method. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 3722.1835 by Long Division Method
The long division method is particularly useful for non-perfect square numbers. This method involves finding the square root step by step. Here is how it is done for 3722.1835:
Step 1: Group the digits of the number in pairs, starting from the decimal point. For 3722.1835, group it as 37, 22, 18, and 35.
Step 2: Find the largest integer whose square is less than or equal to 37. This is 6, because 6² = 36.
Step 3: Subtract 36 from 37, giving a remainder of 1. Bring down the next pair of digits (22), making it 122.
Step 4: Double the current quotient (6) to get 12, and use it as the starting part of the new divisor. Find the largest digit (x) such that 12x * x ≤ 122. The digit is 9, as 129 * 9 = 1161.
Step 5: Subtract 1161 from 1220 to get 59. Bring down the next pair of digits (18), making it 5918.
Step 6: Double the current quotient (69) to get 138, and find the largest digit (x) such that 138x * x ≤ 5918. The digit is 4, as 1384 * 4 = 5536.
Step 7: Subtract 5536 from 5918 to get 382, and bring down the next pair of digits (35), making it 38235.
Step 8: Continue this process until you achieve the desired level of precision.
The quotient obtained is approximately 61.0113.
Square Root of 3722.1835 by Approximation Method
Approximation is another method for estimating the square root, and it is simple to apply. Here is how to approximate the square root of 3722.1835:
Step 1: Identify two closest perfect squares between which 3722.1835 falls. These are 3600 (60²) and 3721 (61²), so √3722.1835 is between 60 and 61.
Step 2: Since 3722.1835 is slightly more than 3721, the square root will be slightly more than 61. Using interpolation or a calculator, the approximate square root is found to be 61.0113.
Common Mistakes and How to Avoid Them in the Square Root of 3722.1835
Students often make mistakes while calculating square roots, such as ignoring the negative square root or skipping steps in the long division method. Let us explore some frequent errors in detail.
Mistake 1
Forgetting about the negative square root
Students should remember that a number has both positive and negative square roots. However, we typically focus on the positive square root for practical applications.
For example, √50 = 7.07, but there is also -7.07, which should not be overlooked.
Square Root of 3722.1835 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3722.1835?
The area of the square is 3722.1835 square units.
Explanation
The area of a square is side².
The side length is given as √3722.1835.
Area = (√3722.1835)² = 3722.1835.
Therefore, the area of the square box is 3722.1835 square units.
Problem 2
A square-shaped building measuring 3722.1835 square feet is built; if each side is √3722.1835, what will be the square feet of half of the building?
1861.09175 square feet
Explanation
To find the area of half of the building, divide the total area by 2.
Dividing 3722.1835 by 2 gives 1861.09175.
So, half of the building measures 1861.09175 square feet.
Problem 3
Calculate √3722.1835 x 5.
305.0565
Explanation
First, find the square root of 3722.1835, which is approximately 61.0113.
Then multiply 61.0113 by 5.
So, 61.0113 x 5 = 305.0565.
Problem 4
What will be the square root of (3722 + 1)?
The square root is 61.
Explanation
Calculate the sum of (3722 + 1) = 3723.
Since 3723 is close to 3721, whose square root is 61, we approximate √3723 ≈ 61.
Therefore, the square root of (3722 + 1) is approximately 61.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3722.1835 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 198.0226 units.
Explanation
Perimeter of a rectangle = 2 × (length + width).
Perimeter = 2 × (√3722.1835 + 38)
= 2 × (61.0113 + 38)
≈ 2 × 99.0113
= 198.0226 units.
FAQ on Square Root of 3722.1835
1.What is √3722.1835 in its simplest form?
2.Calculate the square of 3722.1835.
3.What are some applications of square roots?
4.Is 3722.1835 a perfect square?
5.What is an approximate value of √3722.1835?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 3722.1835?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 3722.1835?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 3722.1835
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4.
- Irrational number: An irrational number cannot be expressed as a simple fraction; it has a non-repeating, non-terminating decimal expansion.
- Long division method: A step-by-step process of dividing numbers to find the square root of non-perfect squares.
- Approximation: Estimating a number or value that is close to the exact amount, often used when finding square roots of non-perfect squares.
- Perfect square: A number that is the square of an integer, such as 1, 4, 9, 16, and so on.
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About BrightChamps in Saudi Arabia
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.
