117 LearnersLast updated on May 26th, 2025
Square Root of 4834
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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 4834.
What is the Square Root of 4834?
The square root is the inverse of the square of the number. 4834 is not a perfect square. The square root of 4834 is expressed in both radical and exponential forms. In the radical form, it is expressed as √4834, whereas (4834)^(1/2) in the exponential form. √4834 ≈ 69.535, 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 4834
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not used; instead, 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 4834 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4834 is broken down into its prime factors.
Step 1: Finding the prime factors of 4834. Breaking it down, we get 2 x 2417, but since 4834 is not a perfect square, it cannot be expressed by pairs of prime factors. Therefore, calculating 4834 using prime factorization is not feasible.
Square Root of 4834 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 4834, we need to group it as 48 and 34.
Step 2: Now we need to find n whose square is less than or equal to 48. We can say n as '6' because 6 x 6 = 36, which is less than 48. The quotient is 6, and after subtracting 36 from 48, the remainder is 12.
Step 3: Now let us bring down 34, making the new dividend 1234. Add the old divisor with the same number, 6 + 6, to get 12, which becomes the new divisor.
Step 4: The new divisor is 12n, so we need to find the value of n.
Step 5: Find 12n x n ≤ 1234. Let us consider n as 9, now 129 x 9 = 1161.
Step 6: Subtract 1161 from 1234; the difference is 73, and the quotient is 69.
Step 7: Since the dividend is less than the 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 7300.
Step 8: Now we need to find the new divisor that is 139 because 1395 x 5 = 6975.
Step 9: Subtracting 6975 from 7300, we get the result 325.
Step 10: Now the quotient is 69.5
Step 11: Continue these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.
So the square root of √4834 ≈ 69.54
Square Root of 4834 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 4834 using the approximation method.
Step 1: Now we have to find the closest perfect square to √4834. The perfect squares closest to 4834 are 4761 (69²) and 4900 (70²). √4834 falls somewhere between 69 and 70.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (4834 - 4761) / (4900 - 4761) = 73 / 139 ≈ 0.525 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 69 + 0.525 ≈ 69.525, so the square root of 4834 is approximately 69.525. 69 + 0.525 ≈ 69.525, so the square root of 4834 is approximately 69.525.
Common Mistakes and How to Avoid Them in the Square Root of 4834
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. 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 has both positive and negative square roots. However, we will be considering only the principal (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.
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 before moving on.
For Example, √(12 + 24) ≠ √12 + √24.
The correct 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; the correct answer is √50 ≈ 7.071.
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, resulting in a wrong answer at the end of the calculation. This may either happen in subtracting or elsewhere.
Square Root of 4834 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4834?
The area of the square is approximately 233,306.2256 square units.
Explanation
The area of the square = side².
The side length is given as √4834.
Area of the square = side² = √4834 x √4834 = 69.54 x 69.54 ≈ 4834.
Therefore, the area of the square box is approximately 4834 square units.
Problem 2
A square-shaped building measuring 4834 square feet is built; if each of the sides is √4834, what will be the square feet of half of the building?
2417 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 4834 by 2, we get 2417.
So half of the building measures 2417 square feet.
Problem 3
Calculate √4834 x 5.
Approximately 347.675
Explanation
The first step is to find the square root of 4834, which is approximately 69.54.
The second step is to multiply 69.54 by 5.
So 69.54 x 5 ≈ 347.675.
Problem 4
What will be the square root of (4834 + 66)?
The square root is approximately 70.
Explanation
To find the square root, we need to find the sum of (4834 + 66). 4834 + 66 = 4900, and √4900 = 70.
Therefore, the square root of (4834 + 66) is ±70.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4834 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 239.08 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√4834 + 50) = 2 × (69.54 + 50) = 2 × 119.54 ≈ 239.08 units.
FAQ on Square Root of 4834
1.What is √4834 in its simplest form?
2.Mention the factors of 4834.
3.Calculate the square of 4834.
4.Is 4834 a prime number?
5.4834 is divisible by?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 4834?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 4834?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 4834
- Square root: A square root is the inverse of a square. Example: 4² = 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.
- 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 the principal square root.
- Prime factorization: Prime factorization is finding which prime numbers multiply together to make the original number.
- Perfect square: A perfect square is a number that can be expressed as the product of an integer with itself. For example, 4, 9, 16, 25, etc., are 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.
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