110 LearnersLast updated on May 26th, 2025
Square Root of 1930
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 1930.
What is the Square Root of 1930?
The square root is the inverse of the square of the number. 1930 is not a perfect square. The square root of 1930 is expressed in both radical and exponential form. In radical form, it is expressed as √1930, whereas (1930)^(1/2) in exponential form. √1930 ≈ 43.923, 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 1930
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 and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1930 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1930 is broken down into its prime factors.
Step 1: Finding the prime factors of 1930 Breaking it down, we get 2 x 5 x 193.
Step 2: Now we found out the prime factors of 1930. The second step is to make pairs of those prime factors. Since 1930 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.
Therefore, calculating 1930 using prime factorization is impossible.
Square Root of 1930 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 1930, we need to group it as 30 and 19.
Step 2: Now we need to find n whose square is less than or equal to 19. We can say n as ‘4’ because 4 x 4 = 16, which is lesser than 19. Now the quotient is 4, and after subtracting 16 from 19, the remainder is 3.
Step 3: Bring down 30, making the new dividend 330. Add the old divisor with the same number 4 + 4 to get 8, which will be our new divisor.
Step 4: Finding a number n such that 8n x n is less than or equal to 330. If we consider n as 3, then 83 x 3 = 249.
Step 5: Subtract 249 from 330, and the difference is 81, with the quotient now being 43.
Step 6: Since the dividend is less than the new 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 8100.
Step 7: Find the new divisor, which is 439, because 439 x 9 = 3951.
Step 8: Subtracting 3951 from 8100 gives us a remainder of 4149.
Step 9: Continue with these steps until you achieve the desired decimal precision.
The result is √1930 ≈ 43.923.
Square Root of 1930 by Approximation Method
The approximation method is another method for finding square roots; it is an easy way to find the square root of a given number. Now let us learn how to find the square root of 1930 using the approximation method.
Step 1: Find the closest perfect square to √1930. The smallest perfect square less than 1930 is 1849, and the largest perfect square greater than 1930 is 2025. √1930 falls somewhere between 43 and 45.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula: (1930 - 1849) / (2025 - 1849) = 0.545.
Adding this to the smallest perfect square root gives us 43 + 0.545 = 43.545, so the square root of 1930 is approximately 43.545.
Common Mistakes and How to Avoid Them in the Square Root of 1930
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we typically use only the positive square root, as it is the required one.
For example, √50 = 7.07, but there is also -7.07, which should not be forgotten.
Square Root of 1930 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1930?
The area of the square is approximately 3726.729 square units.
Explanation
The area of the square = side^2.
The side length is given as √1930.
Area of the square = side^2 = √1930 x √1930 = 43.923 x 43.923 ≈ 1930.
Therefore, the area of the square box is approximately 3726.729 square units.
Problem 2
A square-shaped building measuring 1930 square feet is built; if each of the sides is √1930, what will be the square feet of half of the building?
965 square feet
Explanation
We can divide the given area by 2, as the building is square-shaped.
Dividing 1930 by 2 = we get 965.
So half of the building measures 965 square feet.
Problem 3
Calculate √1930 x 5.
Approximately 219.615.
Explanation
The first step is to find the square root of 1930, which is approximately 43.923.
The second step is to multiply 43.923 with 5.
So 43.923 x 5 ≈ 219.615.
Problem 4
What will be the square root of (1924 + 6)?
The square root is approximately 44.
Explanation
To find the square root, we need to find the sum of (1924 + 6).
1924 + 6 = 1930, and then √1930 ≈ 44.
Therefore, the square root of (1924 + 6) is approximately ±44.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1930 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 163.846 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1930 + 38) = 2 × (43.923 + 38) = 2 × 81.923 = 163.846 units.
FAQ on Square Root of 1930
1.What is √1930 in its simplest form?
2.What are the factors of 1930?
3.Calculate the square of 1930.
4.Is 1930 a prime number?
5.Is 1930 divisible by 2?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 1930?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 1930?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 1930
- 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, 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. This is why it is also known as the principal square root.
- Approximation method: A method used to find an approximate value of a square root, especially when dealing with non-perfect squares.
- Long division method: A step-by-step process used to find the square root of a number, particularly useful for non-perfect squares.
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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
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