118 LearnersLast updated on May 26th, 2025
Square Root of 218
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 218.
What is the Square Root of 218?
The square root is the inverse of the square of the number. 218 is not a perfect square. The square root of 218 is expressed in both radical and exponential form. In the radical form, it is expressed as √218, whereas (218)^(1/2) in the exponential form. √218 ≈ 14.76482, 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 218
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 218 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 218 is broken down into its prime factors.
Step 1: Finding the prime factors of 218 Breaking it down, we get 2 x 109 (109 is a prime number).
Step 2: Now we found out the prime factors of 218. The second step is to make pairs of those prime factors. Since 218 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 218 using prime factorization is not straightforward.
Square Root of 218 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 218, we need to group it as 18 and 2.
Step 2: Find n whose square is less than or equal to 2. We can say n is '1' because 1 x 1 = 1, which is less than 2. Now the quotient is 1 and the remainder is 1.
Step 3: Bring down 18, which is the new dividend. Double the old divisor: 1 + 1 = 2, and use this as the new divisor.
Step 4: Find a digit n such that 2n x n is less than or equal to 118. Let n be 5, now 25 x 5 = 125, which is too large. Instead, 24 x 4 = 96 works.
Step 5: Subtract 96 from 118, resulting in a remainder of 22.
Step 6: 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 2200.
Step 7: Bring down two zeros, making it 2200. Double the quotient: 14, to get 28_ as the new divisor.
Step 8: Find the number to complete the divisor: 282 x 7 = 1974.
Step 9: Subtract 1974 from 2200 to get a remainder of 226.
Step 10: Continue this process to get more decimal places. The quotient so far is 14.7, and continuing will refine the square root of 218.
Square Root of 218 by Approximation Method
The approximation method is another way of finding square roots, and it is an easy method for estimating the square root of a given number. Now let us learn how to find the square root of 218 using the approximation method.
Step 1: Identify the closest perfect squares to √218. The smallest perfect square below 218 is 196 (14^2) and the largest perfect square above 218 is 225 (15^2). Therefore, √218 falls somewhere between 14 and 15.
Step 2: Apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). (218 - 196) / (225 - 196) = 22 / 29 ≈ 0.7586.
Step 3: The approximate value is 14 + 0.7586 = 14.7586, so the square root of 218 is approximately 14.76.
Common Mistakes and How to Avoid Them in the Square Root of 218
Students often make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in the long division method. Let us examine a few common mistakes that students may encounter.
Mistake 1
Forgetting about the Negative Square Root
It's important to remember that a number has both positive and negative square roots. However, we usually consider only the positive square root.
For example, √50 = 7.071, but there is also -7.071, which should not be forgotten.
Mistake 2
Not Adding the Square Root Symbol in Proper Places
Another mistake is not using the square root symbol correctly. To avoid this, students should learn to simplify the numbers inside the square root symbol first before proceeding.
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
Students should be taught to simplify numbers inside the square root to avoid mistakes in identifying the approximate value.
For example, √50 ≠ 7; the correct approximation is √50 ≈ 7.071.
Mistake 4
Confusing the Square Root Symbol with the Cube Root
Students need to understand the difference between cube roots and square roots to 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. Students might skip a step accidentally, leading to a wrong answer. This can happen during subtraction or elsewhere in the process.
Square Root of 218 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √218?
The area of the square is approximately 218 square units.
Explanation
The area of the square = side^2.
The side length is given as √218.
Area of the square = side^2 = √218 x √218 = 218.
Therefore, the area of the square box is approximately 218 square units.
Problem 2
A square-shaped playground measures 218 square feet. If each of the sides is √218, what will be the square feet of half of the playground?
109 square feet
Explanation
We can just divide the given area by 2 as the playground is square-shaped.
Dividing 218 by 2 = 109.
So half of the playground measures 109 square feet.
Problem 3
Calculate √218 x 5.
73.8241
Explanation
The first step is to find the square root of 218, which is approximately 14.76.
The second step is to multiply 14.76 by 5. So 14.76 x 5 ≈ 73.8241.
Problem 4
What will be the square root of (200 + 18)?
The square root is approximately 14.76.
Explanation
To find the square root, we calculate the sum of (200 + 18). 200 + 18 = 218, and then √218 ≈ 14.76.
Therefore, the square root of (200 + 18) is approximately ±14.76.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √218 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 105.52 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√218 + 38) ≈ 2 × (14.76 + 38) ≈ 2 × 52.76 = 105.52 units.
FAQ on Square Root of 218
1.What is √218 in its simplest form?
2.Mention the factors of 218.
3.Calculate the square of 218.
4.Is 218 a prime number?
5.218 is divisible by?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 218?
8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 218?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for the Square Root of 218
- 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, so √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, the positive square root is often more relevant due to real-world applications. This is known as the principal square root.
- Prime factorization: The process of expressing a number as the product of its prime factors, such as 2 x 109 for 218.
- Long division method: A method used to find the square root of a number by dividing it into smaller parts, especially useful for non-perfect squares.
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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
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