125 LearnersLast updated on May 26th, 2025
Square Root of 930
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 such as vehicle design and finance. Here, we will discuss the square root of 930.
What is the Square Root of 930?
The square root is the inverse of squaring a number. 930 is not a perfect square. The square root of 930 is expressed in both radical and exponential form. In the radical form, it is expressed as √930, whereas in exponential form it is (930)^(1/2). √930 ≈ 30.495, 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 930
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 930 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 930 is broken down into its prime factors.
Step 1: Finding the prime factors of 930 Breaking it down, we get 2 x 3 x 5 x 31: 2^1 x 3^1 x 5^1 x 31^1
Step 2: Now we have found the prime factors of 930. Since 930 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating √930 using prime factorization is not feasible.
Square Root of 930 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 930, we need to group it as 30 and 9.
Step 2: Now we need to find n whose square is less than or equal to 9. We can say n is ‘3’ because 3 x 3 = 9. Now the quotient is 3, and after subtracting 9 - 9, the remainder is 0.
Step 3: Bring down 30, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.
Step 4: The new divisor will be 6n. We need to find the value of n such that 6n x n ≤ 30. Let us consider n as 5, now 65 x 5 = 325, which is too large. Instead, try n as 4: 64 x 4 = 256.
Step 5: Subtract 30 from 25, and the difference is 5. The quotient is 3.4.
Step 6: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal allows us to add two zeroes to the dividend. Now the new dividend is 500.
Step 7: Find the new divisor: 69 because 694 x 4 = 276.
Step 8: Subtract 276 from 500, resulting in 224. Step 9: Now the quotient is 30.49.
Step 10: Continue 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 √930 is approximately 30.495.
Square Root of 930 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 930 using the approximation method.
Step 1: We need to find the closest perfect squares to √930.
The smallest perfect square less than 930 is 900, and the largest perfect square greater than 930 is 961.
√930 falls somewhere between 30 and 31.
Step 2: Now we need to apply the formula:
(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula (930 - 900) / (961 - 900) = 30/61 ≈ 0.49.
Adding the initial whole number to the decimal gives us: 30 + 0.49 ≈ 30.49.
Therefore, the square root of 930 is approximately 30.49.
Common Mistakes and How to Avoid Them in the Square Root of 930
Students often make mistakes while finding the square root, such as forgetting about the negative square root and skipping steps in the long division method. Let's look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It's important to remind students that a number has both positive and negative square roots. However, we typically focus on the positive square root, as it is the most commonly used.
For example, √50 = 7.07; there is also -7.07, which should not be overlooked.
Square Root of 930 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √930?
The area of the square is 930 square units.
Explanation
The area of a square = side^2. The side length is given as √930. Area of the square = side^2 = √930 x √930 = 930. Therefore, the area of the square box is 930 square units.
Problem 2
A square-shaped building measuring 930 square feet is built; if each of the sides is √930, what will be the square feet of half of the building?
465 square feet
Explanation
We can simply divide the given area by 2, as the building is square-shaped. Dividing 930 by 2 gives us 465. So half of the building measures 465 square feet.
Problem 3
Calculate √930 x 5.
152.475
Explanation
First, find the square root of 930, which is approximately 30.495.
Then multiply 30.495 by 5.
So, 30.495 x 5 = 152.475.
Problem 4
What will be the square root of (900 + 30)?
The square root is approximately 30.495.
Explanation
To find the square root, first sum (900 + 30) = 930, then √930 ≈ 30.495.
Therefore, the square root of (900 + 30) is approximately ±30.495.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √930 units and the width ‘w’ is 20 units.
The perimeter of the rectangle is approximately 101 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√930 + 20) ≈ 2 × (30.495 + 20) ≈ 2 × 50.495 = 100.99 units.
FAQ on Square Root of 930
1.What is √930 in its simplest form?
2.Mention the factors of 930.
3.Calculate the square of 930.
4.Is 930 a prime number?
5.930 is divisible by?
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 930?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 930?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 930
- Square root: A square root is the inverse of squaring a number. For example, 4^2 = 16, and the inverse is the square root: √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.
- Approximation: An approximation is a value or quantity that is nearly but not exactly correct; it is used when a precise answer is not feasible.
- Long division method: A step-by-step method used to divide numbers to find the square root of non-perfect squares.
- Decimal: A number that includes a whole number and a fractional part, separated by a decimal point, such as 7.86, 8.65, and 9.42.
Explore More algebra
Previous to Square Root of 930
About BrightChamps in Vietnam
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.
