123 LearnersLast updated on May 26th, 2025
Square Root of 2420
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 various fields such as vehicle design and finance. Here, we will discuss the square root of 2420.
What is the Square Root of 2420?
The square root is the inverse of the square of the number. 2420 is not a perfect square. The square root of 2420 is expressed in both radical and exponential form. In the radical form, it is expressed as √2420, whereas (2420)^(1/2) in the exponential form. √2420 ≈ 49.1935, 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 2420
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 2420 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2420 is broken down into its prime factors:
Step 1: Finding the prime factors of 2420 Breaking it down, we get 2 x 2 x 5 x 11 x 11: 2^2 x 5^1 x 11^2
Step 2: Now we found out the prime factors of 2420. The second step is to make pairs of those prime factors. Since 2420 is not a perfect square, therefore the digits of the number can’t be grouped in pair completely. Therefore, calculating 2420 using prime factorization directly for its square root is not straightforward.
Square Root of 2420 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 2420, we need to group it as 20 and 24.
Step 2: Now we need to find n whose square is closest to 24. We can say n is ‘4’ because 4 x 4 = 16, which is less than 24. Now the quotient is 4, after subtracting 24 - 16 the remainder is 8.
Step 3: Now let us bring down 20 which is the new dividend. Add the old divisor (4) with the same number 4 + 4 to get 8, which will be our new divisor.
Step 4: The new divisor will be 8n, we need to find the value of n.
Step 5: The next step is finding 8n × n ≤ 820. Let us consider n as 9, now 89 x 9 = 801.
Step 6: Subtract 820 from 801, the difference is 19, and the quotient is 49.
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 1900.
Step 8: Now we need to find the new divisor, which is 98 because 98 x 9 = 882.
Step 9: Subtracting 882 from 1900, we get the result 1018.
Step 10: Now the quotient is 49.1
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values continue till the remainder is zero.
So the square root of √2420 is approximately 49.19.
Square Root of 2420 by Approximation Method
The approximation method is another method for finding the 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 2420 using the approximation method.
Step 1: Now we have to find the closest perfect square of √2420. The smallest perfect square less than 2420 is 2401, and the largest perfect square more than 2420 is 2500. √2420 falls somewhere between 49 and 50.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square).
Going by the formula (2420 - 2401) ÷ (2500 - 2401) = 19 ÷ 99 = 0.192
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 49 + 0.192 = 49.192, so the square root of 2420 is approximately 49.192.
Common Mistakes and How to Avoid Them in the Square Root of 2420
Students do make mistakes while finding the square root, likewise 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 typically consider only the positive square root, as it is the required one in most practical applications.
For example: √50 = 7.071, there is also -7.071 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before proceeding to the next step.
For Example: √(12+24) = √12 + √24 is incorrect. 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 students 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 incorrect; 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 the 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 occur in subtraction or elsewhere in the process.
Square root of 2420 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2420?
The area of the square is approximately 2420 square units.
Explanation
The area of the square = side^2.
The side length is given as √2420.
Area of the square = side^2 = (√2420)^2 = 2420.
Therefore, the area of the square box is approximately 2420 square units.
Problem 2
A square-shaped building measuring 2420 square feet is built; if each of the sides is √2420, what will be the square feet of half of the building?
1210 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2420 by 2, we get 1210.
So half of the building measures 1210 square feet.
Problem 3
Calculate √2420 × 5.
Approximately 245.965
Explanation
The first step is to find the square root of 2420, which is approximately 49.1935.
The second step is to multiply 49.1935 by 5.
So 49.1935 × 5 ≈ 245.965.
Problem 4
What will be the square root of (2400 + 20)?
The square root is approximately 49.1935.
Explanation
To find the square root, we need to find the sum of (2400 + 20).
2400 + 20 = 2420, and then √2420 is approximately 49.1935.
Therefore, the square root of (2400 + 20) is approximately 49.1935.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2420 units and the width ‘w’ is 20 units.
The perimeter of the rectangle is approximately 138.387 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2420 + 20) ≈ 2 × (49.1935 + 20) ≈ 2 × 69.1935 ≈ 138.387 units.
FAQ on Square Root of 2420
1.What is √2420 in its simplest form?
2.Mention the factors of 2420.
3.Calculate the square of 2420.
4.Is 2420 a prime number?
5.2420 is divisible by?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 2420?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 2420?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 2420
- 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.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that holds more prominence due to its uses in the real world. This is why it is known as the principal square root.
- Prime factorization: The expression of a number as the product of its prime numbers is called prime factorization.
- Decimal: If a number has a whole number and a fraction in a single number, it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
