115 LearnersLast updated on May 26th, 2025
Square Root of 274
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 like vehicle design, finance, and more. Here, we will discuss the square root of 274.
What is the Square Root of 274?
The square root is the inverse of the square of a number. 274 is not a perfect square. The square root of 274 is expressed in both radical and exponential form. In the radical form, it is expressed as √274, whereas in the exponential form, it is (274)^(1/2). √274 ≈ 16.5529, 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 274
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, 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 274 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 274 is broken down into its prime factors:
Step 1: Finding the prime factors of 274
Breaking it down, we get 2 x 137: 2¹ x 137¹
Step 2: Since 274 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √274 using prime factorization is not straightforward.
Square Root of 274 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 274, we need to group it as 74 and 2.
Step 2: Now we need to find n whose square is 2. We can say n as ‘1’ because 1x1 is less 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 74, 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 new divisor will be 2n. We need to find the value of n such that 2n x n ≤ 174. Let us consider n as 6, now 26 x 6 = 156.
Step 5: Subtract 156 from 174; the difference is 18, and the quotient is 16.
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 zeros to the dividend. Now the new dividend is 1800.
Step 7: Now we need to find the new divisor that is 9 because 329 x 9 = 2961.
Step 8: Subtracting 2961 from 1800 is not possible, so we adjust and repeat the process for further precision.
Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no more decimal values; continue till the remainder is zero.
So the square root of √274 ≈ 16.55
Square Root of 274 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 274 using the approximation method.
Step 1: Now we have to find the closest perfect square of √274. The smallest perfect square less than 274 is 256, and the largest perfect square greater than 274 is 289. √274 falls somewhere between 16 and 17.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (274 - 256) / (289 - 256) ≈ 0.55. Using the formula, we identified the decimal point of our square root. The next step is to add the value we got initially to the decimal number, which is 16 + 0.55 = 16.55, so the square root of 274 is approximately 16.55.
Common Mistakes and How to Avoid Them in the Square Root of 274
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in methods like long division. Let us look at a few of those mistakes 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 most practical applications.
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 symbol properly is another mistake that students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving on to other steps.
For example: √(12+24) = √36 is correct, whereas √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 students 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 ≈ 7.071, not 7.
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 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, which results in a wrong answer. This may happen during subtraction or elsewhere in the process.
Square root of 274 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √274?
The area of the square is approximately 750.76 square units.
Explanation
The area of the square = side². The side length is given as √274. Area of the square = side² = √274 x √274 = 16.55 x 16.55 ≈ 274.3025 Therefore, the area of the square box is approximately 750.76 square units.
Problem 2
A square-shaped building measuring 274 square feet is built; if each of the sides is √274, what will be the square feet of half of the building?
137 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped. Dividing 274 by 2 gives us 137. So half of the building measures 137 square feet.
Problem 3
Calculate √274 x 5.
Approximately 82.76
Explanation
The first step is to find the square root of 274, which is approximately 16.55. The second step is to multiply 16.55 by 5. So 16.55 x 5 ≈ 82.76
Problem 4
What will be the square root of (270 + 4)?
The square root is 16.55
Explanation
To find the square root, we need to find the sum of (270 + 4). 270 + 4 = 274, and then √274 ≈ 16.55. Therefore, the square root of (270 + 4) is approximately 16.55.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √274 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 109.1 units.
Explanation
Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√274 + 38) ≈ 2 × (16.55 + 38) ≈ 2 × 54.55 ≈ 109.1 units.
FAQ on Square Root of 274
1.What is √274 in its simplest form?
2.Mention the factors of 274.
3.Calculate the square of 274.
4.Is 274 a prime number?
5.274 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 274?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 274?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 274
- Square root: A square root is the inverse of a square. Example: 4² = 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.
- Perfect square: A perfect square is an integer that is the square of another integer. For example, 144 is a perfect square of 12.
- Decimal: A number that includes a whole number and a fraction in a single number is called a decimal. For example: 7.86, 8.65, and 9.42.
- Long division method: A technique used to find the square root of non-perfect square numbers by using a step-by-step division process.
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About BrightChamps in Bahrain
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.
