126 LearnersLast updated on May 26th, 2025
Square Root of 2404
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 2404.
What is the Square Root of 2404?
The square root is the inverse of the square of the number. 2404 is not a perfect square. The square root of 2404 is expressed in both radical and exponential forms. In the radical form, it is expressed as √2404, whereas in exponential form it is (2404)^(1/2). √2404 ≈ 49.034, 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 2404
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 2404 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2404 is broken down into its prime factors.
Step 1: Finding the prime factors of 2404 Breaking it down, we get 2 × 2 × 601: 2² × 601
Step 2: Since 2404 is not a perfect square, we can't group the digits into pairs.
Therefore, calculating 2404 using prime factorization is impossible.
Square Root of 2404 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 2404, we group it as 24 and 04.
Step 2: Now we need to find n whose square is less than or equal to 24. We can say n is 4 because 4 × 4 = 16, which is less than 24. The quotient is 4, and the remainder is 24 - 16 = 8.
Step 3: Bring down 04 to make the new dividend 804. Add the old divisor (4) with the same number, 4 + 4 = 8, which will be our new divisor's tens digit.
Step 4: We need to find a number n such that (80 + n) × n ≤ 804. Let n be 9, because 89 × 9 = 801.
Step 5: Subtract 801 from 804. The new remainder is 3.
Step 6: Since the remainder is less than the divisor, add a decimal point and two zeroes to the dividend. Now the new dividend is 300.
Step 7: The next divisor will be (89 × 10) + n, we need n such that (890 + n) × n ≤ 300, leading us to n as 0. Repeat these steps until the desired precision is achieved.
The quotient will approximate to √2404 = 49.034.
Square Root of 2404 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 2404 using the approximation method.
Step 1: Find the closest perfect squares around √2404. The smallest perfect square near 2404 is 2401, and the largest is 2500. √2404 falls between √2401 = 49 and √2500 = 50.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (2404 - 2401) / (2500 - 2401) = 3 / 99 ≈ 0.03
Add this to 49 to get the approximate square root: 49 + 0.03 = 49.03.
Common Mistakes and How to Avoid Them in the Square Root of 2404
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. Let's look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we usually consider only the positive square root, as it is more commonly used.
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 people make. It's important to simplify the numbers inside the square root before proceeding.
For example: √(12 + 24) ≠ √12 + √24. The correct usage is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
Students should be taught to simplify the numbers inside the square root first. This helps avoid mistakes in 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
It's important to differentiate between cube roots and square roots to avoid errors.
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, and students might skip a step accidentally, resulting in a wrong answer. This may happen in subtraction or elsewhere.
Square Root of 2404 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2404?
The area of the square is approximately 5777.632 square units.
Explanation
The area of the square = side².
The side length is given as √2404.
Area of the square = side² = √2404 × √2404 ≈ 49.034 × 49.034 ≈ 5777.632
Therefore, the area of the square box is approximately 5777.632 square units.
Problem 2
A square-shaped garden measures 2404 square feet. If each side is √2404, what will be the square feet of half of the garden?
1202 square feet
Explanation
We can just divide the given area by 2 since the garden is square-shaped.
Dividing 2404 by 2, we get 1202.
So half of the garden measures 1202 square feet.
Problem 3
Calculate √2404 × 5.
Approximately 245.17
Explanation
First, find the square root of 2404, which is approximately 49.034.
Then multiply 49.034 by 5. 49.034 × 5 ≈ 245.17
Problem 4
What will be the square root of (2400 + 4)?
The square root is approximately 49.034
Explanation
To find the square root, we need to find the sum of (2400 + 4) 2400 + 4 = 2404, and then √2404 ≈ 49.034
Therefore, the square root of (2400 + 4) is approximately ±49.034
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √2404 units and the width ‘w’ is 40 units.
Approximately 178.068 units
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2404 + 40) ≈ 2 × (49.034 + 40) ≈ 2 × 89.034 ≈ 178.068 units.
FAQ on Square Root of 2404
1.What is √2404 in its simplest form?
2.Mention the factors of 2404.
3.Calculate the square of 2404.
4.Is 2404 a prime number?
5.2404 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 2404?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 2404?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 2404
- 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 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, but the positive square root is more commonly used and is known as the principal square root.
- Prime factorization: The process of expressing a number as a product of its prime factors.
- Long division method: A step-by-step approach used to find the square root of 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.
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