124 LearnersLast updated on May 26th, 2025
Square Root of 204
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 fields such as vehicle design and finance. Here, we will discuss the square root of 204.
What is the Square Root of 204?
The square root is the inverse of the square of the number. 204 is not a perfect square. The square root of 204 is expressed in both radical and exponential form. In the radical form, it is expressed as √204, whereas (204)^(1/2) is in exponential form. √204 ≈ 14.28286, 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 204
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 and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 204 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 204 is broken down into its prime factors.
Step 1: Finding the prime factors of 204 Breaking it down, we get 2 x 2 x 3 x 17: 2^2 x 3^1 x 17^1
Step 2: Now we found out the prime factors of 204. The second step is to make pairs of those prime factors. Since 204 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 204 using prime factorization is not straightforward.
Square Root of 204 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 204, we need to group it as 04 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 x 1 is less than or equal to 2. The quotient is 1, and subtracting 1 from 2 gives a remainder of 1.
Step 3: Now let us bring down 04, making the new dividend 104. Add the old divisor with the same number 1 + 1 to get 2, which will be our new divisor.
Step 4: The new divisor will be 2n, where we need to find the value of n.
Step 5: The next step is finding 2n x n ≤ 104. Let us consider n as 4; now 24 x 4 = 96.
Step 6: Subtract 96 from 104, the difference is 8, and the quotient is 14.
Step 7: Since the remainder 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 800.
Step 8: Find the new divisor, which is 28 because 284 x 4 = 1136.
Step 9: Subtracting 1136 from 8000 gives us 164. Step 10: Now the quotient is 14.2
Step 11: Continue this process until you reach two decimal places or until the remainder is zero.
So the square root of √204 is approximately 14.28.
Square Root of 204 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 204 using the approximation method.
Step 1: Find the closest perfect squares to √204. The smallest perfect square less than 204 is 196, and the largest perfect square greater than 204 is 225. √204 falls between 14 and 15.
Step 2: Now, we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula, (204 - 196) / (225 - 196) ≈ 0.28 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 14 + 0.28 = 14.28, so the square root of 204 is approximately 14.28.
Common Mistakes and How to Avoid Them in the Square Root of 204
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in long division, etc. Let us look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we usually consider only the principal square root, which is positive.
For example, √50 = 7.07 also has a negative counterpart, -7.07, which should not be overlooked.
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 before moving to the next step.
For example, √(12 + 24) = √36 is correct, while √12 + √24 is incorrect.
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 ≈ 7.071067, not simply 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube roots and square roots 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, resulting in a wrong answer. This may happen in subtraction or elsewhere.
Square Root of 204 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √204?
The area of the square is approximately 204 square units.
Explanation
The area of the square = side^2.
The side length is given as √204.
Area of the square = side^2 = √204 x √204 = 204.
Therefore, the area of the square box is approximately 204 square units.
Problem 2
A square-shaped building measuring 204 square feet is built. If each of the sides is √204, what will be the square feet of half of the building?
102 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 204 by 2 gives us 102.
So half of the building measures 102 square feet.
Problem 3
Calculate √204 x 5.
Approximately 71.41
Explanation
The first step is to find the square root of 204, which is approximately 14.28.
The second step is to multiply 14.28 by 5. So, 14.28 x 5 ≈ 71.41.
Problem 4
What will be the square root of (198 + 6)?
The square root is 14.
Explanation
To find the square root, we need to find the sum of (198 + 6). 198 + 6 = 204, and then √204 ≈ 14.28.
Therefore, the square root of (198 + 6) is approximately ±14.28.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √204 units and the width ‘w’ is 20 units.
We find the perimeter of the rectangle as approximately 68.56 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√204 + 20) = 2 × (14.28 + 20) = 2 × 34.28 ≈ 68.56 units.
FAQ on Square Root of 204
1.What is √204 in its simplest form?
2.Mention the factors of 204.
3.Calculate the square of 204.
4.Is 204 a prime number?
5.204 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 204?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 204?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 204
- 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.
- 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 factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 204 is 2 x 2 x 3 x 17.
- Long division method: A step-by-step method used to find the square root of non-perfect squares by dividing and averaging.
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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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