122 LearnersLast updated on May 26th, 2025
Square Root of 2262
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 2262.
What is the Square Root of 2262?
The square root is the inverse of the square of the number. 2262 is not a perfect square. The square root of 2262 is expressed in both radical and exponential form. In the radical form, it is expressed as √2262, whereas (2262)^(1/2) in the exponential form. √2262 ≈ 47.5533, 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 2262
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 2262 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2262 is broken down into its prime factors.
Step 1: Finding the prime factors of 2262 Breaking it down, we get 2 x 3 x 3 x 3 x 3 x 7: 2^1 x 3^4 x 7^1
Step 2: Now that we have found the prime factors of 2262, the second step is to make pairs of those prime factors. Since 2262 is not a perfect square, therefore the digits of the number can’t be grouped into pairs.
Therefore, calculating 2262 using prime factorization is impractical for finding the exact square root.
Square Root of 2262 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 2262, we need to group it as 22 and 62.
Step 2: Now we need to find n whose square is closest to 22. We can say n is ‘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 62, which is the new dividend. Add the old divisor with the same number: 4 + 4, we get 8, which will be our new divisor.
Step 4: The new divisor will be the sum of the current divisor and the quotient, so we get 8n as the new divisor. We need to find the value of n.
Step 5: The next step is finding 8n x n ≤ 662. Let us consider n as 8, now 88 x 8 = 704 which is greater than 662, so we take n as 7.
Step 6: Subtract 662 from 609 (87 x 7 = 609), the difference is 53, 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 5300.
Step 8: Now we need to find the new divisor that is 951 because 951 x 5 = 4755.
Step 9: Subtracting 4755 from 5300, we get the result 545.
Step 10: Now the quotient is 47.5.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue till the remainder is zero.
So the square root of √2262 is approximately 47.55.
Square Root of 2262 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 2262 using the approximation method.
Step 1: Now we have to find the closest perfect square of √2262. The smallest perfect square of 2262 is 2025, and the largest perfect square is 2304. √2262 falls somewhere between 45 and 48.
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 (2262 - 2025) ÷ (2304 - 2025) = 237 ÷ 279 ≈ 0.85.
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 47 + 0.55 = 47.55.
So the square root of 2262 is approximately 47.55.
Common Mistakes and How to Avoid Them in the Square Root of 2262
Students do make mistakes while finding the square root, such as forgetting about the negative square root or 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 an incorrect 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 ≈ 7.071.
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 keep away from 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 calculation. This may either happen in subtracting or elsewhere.
Square root of 2262 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2262?
The area of the square is 5112.606 square units.
Explanation
The area of the square = side^2.
The side length is given as √2262.
Area of the square = side^2 = √2262 x √2262 ≈ 47.5533 x 47.5533 = 2262.
Therefore, the area of the square box is 2262 square units.
Problem 2
A square-shaped building measuring 2262 square feet is built; if each of the sides is √2262, what will be the square feet of half of the building?
1131 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2262 by 2 = we get 1131.
So half of the building measures 1131 square feet.
Problem 3
Calculate √2262 x 5.
237.77
Explanation
The first step is to find the square root of 2262, which is approximately 47.55.
The second step is to multiply 47.55 with 5.
So 47.55 x 5 ≈ 237.77.
Problem 4
What will be the square root of (2262 + 6)?
The square root is approximately 48.
Explanation
To find the square root, we need to find the sum of (2262 + 6).
2262 + 6 = 2268, and then √2268 ≈ 47.63.
Therefore, the square root of (2262 + 6) is approximately 47.63.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √2262 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 171.1 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2262 + 38) ≈ 2 × (47.55 + 38) = 2 × 85.55 = 171.1 units.
FAQ on Square Root of 2262
1.What is √2262 in its simplest form?
2.Mention the factors of 2262.
3.Calculate the square of 2262.
4.Is 2262 a prime number?
5.2262 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 2262?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 2262?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 2262
- 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 a positive square root that has more prominence due to its uses in the real world. That is why it is also known as the principal square root.
- Long division method: A method used to find the square root of non-perfect squares by pairing digits from right to left and estimating successive digits of the quotient.
- Approximation method: A method for estimating the square root by finding the nearest perfect squares and interpolating to find an approximate value.
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About BrightChamps in Saudi Arabia
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.
