122 LearnersLast updated on May 26th, 2025
Square Root of 227
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 227.
What is the Square Root of 227?
The square root is the inverse of the square of the number. 227 is not a perfect square. The square root of 227 is expressed in both radical and exponential form. In radical form, it is expressed as √227, whereas (227)^(1/2) in exponential form. √227 ≈ 15.0665, 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 227
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 227 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 227 is broken down into its prime factors.
Step 1: Finding the prime factors of 227 227 is a prime number, so it cannot be broken down into smaller prime factors. Since 227 is not a perfect square, calculating √227 using prime factorization is not feasible.
Square Root of 227 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 227, we need to group it as 27 and 2.
Step 2: Now we need to find n whose square is ≤ 2. We can say n as ‘1’ because 1 × 1 is lesser than or equal to 2. Now the quotient is 1, after subtracting 1 from 2, the remainder is 1.
Step 3: Now let us bring down 27, which is the new dividend. Add the old divisor with the same number 1 + 1, we get 2, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor; we need to find the value of n.
Step 5: The next step is finding 2n × n ≤ 127. Let's consider n as 5, now 25 × 5 = 125.
Step 6: Subtract 127 from 125, the difference is 2, and the quotient is 15.
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 200.
Step 8: Now we need to find the new divisor, which is 301 because 301 × 0 = 0.
Step 9: Subtracting 0 from 200, we get the result 200, and we continue the process.
Step 10: Now the quotient is 15.0
Step 11: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.
So the square root of √227 is approximately 15.066.
Square Root of 227 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 227 using the approximation method.
Step 1: Now we have to find the closest perfect square of √227. The smallest perfect square less than 227 is 225, and the largest perfect square greater than 227 is 256. √227 falls somewhere between 15 and 16.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (227 - 225) / (256 - 225) = 2 / 31 ≈ 0.065. 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 15 + 0.065 ≈ 15.065, so the square root of 227 is approximately 15.065.
Common Mistakes and How to Avoid Them in the Square Root of 227
Students do make mistakes while finding the square root, like 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 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 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 the wrong 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 sum. This may either happen in subtracting or elsewhere.
Square root of 227 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √227?
The area of the square is approximately 227 square units.
Explanation
The area of the square = side².
The side length is given as √227.
Area of the square = side² = √227 × √227 = 227.
Therefore, the area of the square box is approximately 227 square units.
Problem 2
A square-shaped building measuring 227 square feet is built; if each of the sides is √227, what will be the square feet of half of the building?
113.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 227 by 2 = we get 113.5.
So half of the building measures 113.5 square feet.
Problem 3
Calculate √227 × 5.
Approximately 75.33
Explanation
The first step is to find the square root of 227, which is approximately 15.066, the second step is to multiply 15.066 by 5.
So 15.066 × 5 ≈ 75.33.
Problem 4
What will be the square root of (225 + 2)?
The square root is approximately 15.066
Explanation
To find the square root, we need to find the sum of (225 + 2).
225 + 2 = 227, and then √227 ≈ 15.066.
Therefore, the square root of (225 + 2) is approximately ±15.066.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √227 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 106.13 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√227 + 38)
= 2 × (15.066 + 38)
= 2 × 53.066
≈ 106.13 units.
FAQ on Square Root of 227
1.What is √227 in its simplest form?
2.Mention the factors of 227.
3.Calculate the square of 227.
4.Is 227 a prime number?
5.227 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 227?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 227?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 227
- 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 number: A prime number is a number greater than 1 that has no divisors other than 1 and itself. Example: 227 is a prime number.
- Decimal approximation: When the square root of a number is not a perfect square, its decimal approximation is used to represent its value. Example: √227 ≈ 15.0665.
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About BrightChamps in Qatar
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.
