119 LearnersLast updated on May 26th, 2025
Square Root of 2240
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, finance, etc. Here, we will discuss the square root of 2240.
What is the Square Root of 2240?
The square root is the inverse of the square of a number. 2240 is not a perfect square. The square root of 2240 can be expressed in both radical and exponential form. In radical form, it is expressed as √2240, whereas in exponential form it is expressed as (2240)^(1/2). √2240 ≈ 47.331, 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 2240
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods such as long division and approximation are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2240 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2240 is broken down into its prime factors.
Step 1: Finding the prime factors of 2240 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 5 x 7 = 2^5 x 5 x 7
Step 2: Now we have found the prime factors of 2240. The next step is to make pairs of those prime factors. Since 2240 is not a perfect square, the digits of the number cannot be grouped into pairs evenly.
Therefore, calculating 2240 using prime factorization is not straightforward.
Square Root of 2240 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 2240, we need to group it as 40 and 22.
Step 2: Now we need to find n whose square is less than or equal to 22. We can say n as '4' because 4 x 4 = 16, which is less than 22. Now the quotient is 4, and after subtracting 16 from 22, the remainder is 6.
Step 3: Now let us bring down 40, making the new dividend 640. Add the old divisor with the same number, 4 + 4, to get 8, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we have 8n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 8n × n ≤ 640. Let us consider n as 7, now 87 x 7 = 609.
Step 6: Subtract 609 from 640, the difference is 31, and the quotient is 47.
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 3100.
Step 8: Now find the new divisor, 94, because 944 x 4 = 3776, which is too large, so try 93, and 932 x 2 = 1864, which fits.
Step 9: Subtracting 1864 from 3100 results in 1236.
Step 10: Continue these steps until you get two numbers after the decimal point. Suppose there is no decimal value; continue until the remainder is zero.
So the square root of √2240 ≈ 47.33.
Square Root of 2240 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 2240 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √2240. The smallest perfect square below 2240 is 2025 (45^2) and the largest perfect square above 2240 is 2304 (48^2). √2240 falls somewhere between 45 and 48.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (greater perfect square - smallest perfect square).
Using the formula: (2240 - 2025) ÷ (2304 - 2025) = 215 ÷ 279 ≈ 0.77.
Add this value to the lower bound of our range: 45 + 0.77 = 45.77, which is an approximation.
So we refine further to 47.33.
Common Mistakes and How to Avoid Them in the Square Root of 2240
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in 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 usually consider only the positive square root, as it is the required one in most practical cases.
For example: √225 = 15, but there is also -15, which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root symbol 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 moving to the next step.
For Example: √(12 + 24) ≠ √12 + √24. The correct method is √(12 + 24) = √36 = 6.
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; 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, which results in a wrong answer at the end. This may happen during subtraction or elsewhere in the process.
Square Root of 2240 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2240?
The area of the square is approximately 2240 square units.
Explanation
The area of the square = side².
The side length is given as √2240.
Area of the square = side² = √2240 × √2240 = 2240.
Therefore, the area of the square box is approximately 2240 square units.
Problem 2
A square-shaped building measuring 2240 square feet is built; if each of the sides is √2240, what will be the square feet of half of the building?
1120 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2240 by 2 = 1120.
So half of the building measures 1120 square feet.
Problem 3
Calculate √2240 × 5.
236.655
Explanation
The first step is to find the square root of 2240, which is approximately 47.331.
The second step is to multiply 47.331 by 5.
So, 47.331 × 5 ≈ 236.655.
Problem 4
What will be the square root of (2236 + 4)?
The square root is approximately 48.
Explanation
To find the square root, we need to find the sum of (2236 + 4).
2236 + 4 = 2240, and then √2240 ≈ 47.331.
Therefore, the square root of (2236 + 4) is approximately ±47.331.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2240 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 170.662 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2240 + 38) = 2 × (47.331 + 38) = 2 × 85.331 ≈ 170.662 units.
FAQ on Square Root of 2240
1.What is √2240 in its simplest form?
2.Mention the factors of 2240.
3.Calculate the square of 2240.
4.Is 2240 a prime number?
5.2240 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 2240?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 2240?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 2240
- 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, which 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 an integer that is the square of an integer. For example, 9 is a perfect square because it is 3^2.
- Prime factorization: The process of expressing a number as the product of its prime factors.
- Long division method: A method used to find the square root of numbers, especially non-perfect squares, through a systematic division process.
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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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