120 LearnersLast updated on May 26th, 2025
Square Root of 674
If a number is multiplied by itself, the result is a square. The inverse of squaring a number is taking the square root. The square root is used in various fields such as engineering, physics, and finance. Here, we will discuss the square root of 674.
What is the Square Root of 674?
The square root is the inverse operation of squaring a number. 674 is not a perfect square. The square root of 674 is expressed in both radical and exponential forms. In the radical form, it is expressed as √674, whereas in the exponential form, it is expressed as (674)^(1/2). √674 ≈ 25.929, 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 674
The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers like 674, methods such as the long-division method and approximation method are used. Let us explore these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 674 by Prime Factorization Method
Prime factorization involves expressing a number as the product of its prime factors. However, 674 is not a perfect square, and its prime factors cannot be paired to simplify its square root. Thus, calculating √674 using prime factorization directly is not feasible.
Square Root of 674 by Long Division Method
The long division method is often used for calculating the square root of non-perfect square numbers. Below are the steps for using this method:
Step 1: Group the digits of 674 from right to left. For 674, group it as 74 and 6.
Step 2: Find the number whose square is less than or equal to 6. This number is 2, since 2 × 2 = 4. Subtract 4 from 6 to get a remainder of 2.
Step 3: Bring down 74 to make it 274 as the new dividend. Double the previous divisor (2) to get 4.
Step 4: Find a digit n such that 4n × n is less than or equal to 274. The appropriate n is 6, since 46 × 6 = 276, which is too large, so we use n = 5, giving 45 × 5 = 225.
Step 5: Subtract 225 from 274 to get 49.
Step 6: Since the remainder is less than the divisor, add a decimal point and bring down double zeros, making it 4900.
Step 7: Find the new divisor and continue the process to reach a further decimal precision.
The square root of 674 using the long division method is approximately 25.929.
Square Root of 674 by Approximation Method
The approximation method is another approach to finding the square root of a number. Here’s how to approximate the square root of 674:
Step 1: Identify the closest perfect squares to 674. The closest perfect squares are 625 (25²) and 676 (26²). √674 falls between 25 and 26.
Step 2: Use the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). (674 - 625) ÷ (676 - 625) = 0.96 Adding this to 25, we get 25 + 0.96 = 25.96.
Therefore, the approximate square root of 674 is 25.96.
Common Mistakes and How to Avoid Them in the Square Root of 674
Students frequently make mistakes when calculating square roots, such as ignoring the negative square root, misunderstanding methods, etc. Here are some common mistakes to avoid:
Mistake 1
Forgetting about the negative square root
Students should remember that a number has both positive and negative square roots. However, typically the focus is on the positive square root.
For example, √50 = 7.07 also has a negative counterpart, -7.07, which should not be ignored in some contexts.
Mistake 2
Not adding square root symbol in proper places
Misplacing the square root symbol is a common error. Students should ensure calculations inside the square root are simplified before proceeding.
For example, √(12 + 24) = √36, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
Simplifying numbers inside the square root is crucial to avoid errors in approximation. For instance, √50 ≠ 7; rather, it is approximately 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Proper distinction between square root and cube root symbols is necessary. For instance, √8 and ∛8 are different and should not be confused.
Mistake 5
Making mistakes in long division
The long division method involves multiple steps, and skipping any can lead to incorrect results. Careful attention to each step, particularly subtraction and bringing down numbers, is essential.
Square Root of 674 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √674?
The area of the square is approximately 674 square units.
Explanation
The area of the square = side².
The side length is given as √674.
Area of the square = side² = √674 × √674 = 674.
Therefore, the area of the square box is approximately 674 square units.
Problem 2
A square-shaped building measuring 674 square feet is built; if each of the sides is √674, what will be the square feet of half of the building?
337 square feet
Explanation
Since the building is square-shaped, simply divide the given area by 2.
Dividing 674 by 2 gives us 337.
So half of the building measures 337 square feet.
Problem 3
Calculate √674 × 5.
Approximately 129.65
Explanation
First, find the square root of 674, which is approximately 25.929.
Then multiply 25.929 by 5.
So, 25.929 × 5 ≈ 129.65.
Problem 4
What will be the square root of (400 + 274)?
The square root is 26.
Explanation
To find the square root, first sum (400 + 274).
400 + 274 = 674, and then √674 ≈ 25.929, rounded to the nearest whole number is 26.
Therefore, the square root of (400 + 274) is approximately 26.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √674 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 151.86 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√674 + 50)
≈ 2 × (25.929 + 50)
≈ 2 × 75.929
≈ 151.86 units.
FAQ on Square Root of 674
1.What is √674 in its simplest form?
2.Mention the factors of 674.
3.Calculate the square of 674.
4.Is 674 a prime number?
5.674 is divisible by?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 674?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 674?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for the Square Root of 674
- Square root: The square root is the inverse operation of squaring a number. For example, if 5² = 25, then √25 = 5.
- Irrational number: An irrational number cannot be expressed as a simple fraction. The decimal form of an irrational number is non-repeating and non-terminating.
- Principal square root: A number has both positive and negative square roots, but typically the positive square root is used, known as the principal square root.
- Approximation: This is a method used to find an estimated value that is near the actual value. For square roots, approximation methods help find values for non-perfect squares.
- Long division method: A systematic method of finding the square root of a number by dividing, multiplying, and subtracting in a structured manner, step by step.
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About BrightChamps in United Arab Emirates
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.
