123 LearnersLast updated on May 26th, 2025
Square Root of 4850
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 4850.
What is the Square Root of 4850?
The square root is the inverse of the square of the number. 4850 is not a perfect square. The square root of 4850 is expressed in both radical and exponential form. In the radical form, it is expressed as √4850, whereas (4850)^(1/2) in the exponential form. √4850 ≈ 69.607, 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 4850
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 4850 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4850 is broken down into its prime factors.
Step 1: Finding the prime factors of 4850
Breaking it down, we get 2 x 5 x 5 x 97: 2^1 x 5^2 x 97^1
Step 2: Now we found out the prime factors of 4850. The second step is to make pairs of those prime factors. Since 4850 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 4850 using prime factorization is impossible.
Square Root of 4850 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 4850, we group it as 50 and 48.
Step 2: Now we need to find n whose square is less than or equal to 48. We can say n is ‘6’ because 6 x 6 = 36 is less than 48. Now the quotient is 6, and after subtracting 36 from 48, the remainder is 12.
Step 3: Now let us bring down 50, which is the new dividend. Add the old divisor with the same number, 6 + 6, to get 12, which will be our new divisor.
Step 4: We need to find a number, n, such that 12n x n ≤ 1250. Let n = 9, then 12 x 9 x 9 = 1089.
Step 5: Subtract 1089 from 1250, and the difference is 161. The quotient is now 69.
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 16100.
Step 7: Find the new divisor, which is 139, because 1399 x 9 = 12591.
Step 8: Subtracting 12591 from 16100, we get the result 3509.
Step 9: Now the quotient is 69.6.
Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.
So the square root of √4850 is approximately 69.60.
Square Root of 4850 by Approximation Method
The approximation method is another method for finding square roots, and 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 4850 using the approximation method.
Step 1: Now we have to find the closest perfect square of √4850. The smallest perfect square less than 4850 is 4624 (68^2), and the largest perfect square more than 4850 is 4900 (70^2). √4850 falls somewhere between 68 and 70.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Applying the formula: (4850 - 4624) / (4900 - 4624) = 226 / 276 ≈ 0.8188. 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 68 + 0.8188 ≈ 68.82. Thus, the square root of 4850 is approximately 69.61.
Common Mistakes and How to Avoid Them in the Square Root of 4850
Students do make mistakes while finding the square root, like forgetting about the negative square root, 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 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 avoid 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 4850 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4850?
The area of the square is approximately 4850 square units.
Explanation
The area of the square = side^2.
The side length is given as √4850.
Area of the square = side^2 = √4850 x √4850 = 4850.
Therefore, the area of the square box is approximately 4850 square units.
Problem 2
A square-shaped garden measuring 4850 square feet is built. If each of the sides is √4850, what will be the square feet of half of the garden?
2425 square feet
Explanation
We can just divide the given area by 2 since the garden is square-shaped.
Dividing 4850 by 2, we get 2425.
So half of the garden measures 2425 square feet.
Problem 3
Calculate √4850 x 5.
Approximately 348.035
Explanation
The first step is to find the square root of 4850, which is approximately 69.607.
The second step is to multiply 69.607 by 5.
So 69.607 x 5 ≈ 348.035.
Problem 4
What will be the square root of (4850 + 50)?
Approximately 70
Explanation
To find the square root, we need to find the sum of (4850 + 50). 4850 + 50 = 4900, and then √4900 = 70.
Therefore, the square root of (4850 + 50) is ±70.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4850 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 239.214 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√4850 + 50) ≈ 2 × (69.607 + 50) = 2 × 119.607 = approximately 239.214 units.
FAQ on Square Root of 4850
1.What is √4850 in its simplest form?
2.Mention the factors of 4850.
3.Calculate the square of 4850.
4.Is 4850 a prime number?
5.4850 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 4850?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 4850?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 4850
- 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 that 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.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because it is 4^2.
- Long division method: A method used to find the square root of non-perfect squares by dividing and averaging.
- Approximation: The process of finding a value that is close to the actual value but easier to work with.
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Jaskaran Singh Saluja
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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.
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