127 LearnersLast updated on May 26th, 2025
Square Root of 211
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 211.
What is the Square Root of 211?
The square root is the inverse of the square of the number. 211 is not a perfect square. The square root of 211 is expressed in both radical and exponential forms. In the radical form, it is expressed as √211, whereas (211)^(1/2) in the exponential form. √211 ≈ 14.525839, 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 211
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 method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 211 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 211 is broken down into its prime factors.
Step 1: Finding the prime factors of 211 211 is a prime number, so it cannot be broken down into smaller prime factors.
Since 211 is not a perfect square, calculating √211 using prime factorization is not feasible.
Square Root of 211 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 211, we need to group it as 11 and 2.
Step 2: Now we need to find n whose square is less than or equal to 2. We can say n is '1' because 1 × 1 is less than or equal to 2. Now the quotient is 1; after subtracting 1 × 1 from 2, the remainder is 1.
Step 3: Now let us bring down 11, which is the new dividend. Add the old divisor with the same number 1 + 1 to get 2, which will be our new divisor.
Step 4: The next step is finding 2n × n ≤ 111. Let us consider n as 5, now 25 × 5 = 125.
Step 5: Since 125 is greater than 111, try n as 4, now 24 × 4 = 96.
Step 6: Subtract 96 from 111; the difference is 15, and the quotient becomes 14.
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 1500.
Step 8: Now we need to find the new divisor that is 289 because 289 × 5 = 1445.
Step 9: Subtracting 1445 from 1500, we get the result 55.
Step 10: Now the quotient is 14.5.
Step 11: Continue doing these steps until we get the desired precision.
So the square root of √211 is approximately 14.525839.
Square Root of 211 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 211 using the approximation method.
Step 1: Now we have to find the closest perfect square of √211. The smallest perfect square less than 211 is 196 (14^2), and the largest perfect square greater than 211 is 225 (15^2). √211 falls somewhere between 14 and 15.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (211 - 196) / (225 - 196) = 15 / 29 ≈ 0.517. Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the integer, which is 14 + 0.517 ≈ 14.517.
Therefore, the square root of 211 is approximately 14.525839.
Common Mistakes and How to Avoid Them in the Square Root of 211
Students do make mistakes while finding the square root, such as 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 ≈ 7.071067.
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 211 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √211?
The area of the square is 211 square units.
Explanation
The area of the square = side^2.
The side length is given as √211.
Area of the square = side^2 = √211 × √211 = 211.
Therefore, the area of the square box is 211 square units.
Problem 2
A square-shaped building measuring 211 square feet is built; if each of the sides is √211, what will be the square feet of half of the building?
105.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 211 by 2, we get 105.5.
So half of the building measures 105.5 square feet.
Problem 3
Calculate √211 × 5.
Approximately 72.63
Explanation
The first step is to find the square root of 211, which is approximately 14.525839.
The second step is to multiply 14.525839 with 5. So 14.525839 × 5 ≈ 72.63.
Problem 4
What will be the square root of (211 + 14)?
The square root is approximately 15
Explanation
To find the square root, we need to find the sum of (211 + 14). 211 + 14 = 225, and then √225 = 15.
Therefore, the square root of (211 + 14) is ±15.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √211 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 105.05 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√211 + 38) = 2 × (14.525839 + 38) = 2 × 52.525839 ≈ 105.05 units.
FAQ on Square Root of 211
1.What is √211 in its simplest form?
2.Is 211 a perfect square?
3.Calculate the square of 211.
4.Is 211 a prime number?
5.211 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 211?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 211?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 211
- 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.
- Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
- Long division method: A method used to find the square root of non-perfect squares by a systematic division process.
- Approximation method: A method used to estimate the square root of a number by identifying its closest perfect squares and calculating the decimal value.
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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.
