124 LearnersLast updated on May 26th, 2025
Square Root of 754
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 754.
What is the Square Root of 754?
The square root is the inverse of the square of the number. 754 is not a perfect square. The square root of 754 is expressed in both radical and exponential form. In the radical form, it is expressed as √754, whereas (754)^(1/2) in the exponential form. √754 ≈ 27.459, 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 754
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 754 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 754 is broken down into its prime factors.
Step 1: Finding the prime factors of 754 Breaking it down, we get 2 x 13 x 29.
Step 2: Now we found out the prime factors of 754. The second step is to make pairs of those prime factors. Since 754 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.
Therefore, calculating 754 using prime factorization is impossible.
Square Root of 754 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 754, we need to group it as 54 and 7.
Step 2: Now we need to find n whose square is less than or equal to 7. We can say n is ‘2’ because 2 x 2 = 4, which is less than 7. Now the quotient is 2 and the remainder is 3 after subtracting 4 from 7.
Step 3: Now let us bring down 54, making it the new dividend. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor.
Step 4: We need to find 4n × n ≤ 354. Let us consider n as 7. Now 47 x 7 = 329.
Step 5: Subtract 329 from 354. The difference is 25, and the quotient is 27.
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 2500.
Step 7: Now we need to find the new divisor. Let’s consider 549 x 4 = 2196.
Step 8: Subtracting 2196 from 2500, we get the result 304.
Step 9: Now the quotient is 27.4.
Step 10: Continue doing these steps until we get two numbers after the decimal point. If there is no remainder, continue till the remainder is zero.
So the square root of √754 is approximately 27.459.
Square Root of 754 by Approximation Method
Approximation method is another method for finding the 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 754 using the approximation method.
Step 1: Now we have to find the closest perfect square of √754.
The smallest perfect square less than 754 is 729, and the largest perfect square greater than 754 is 784. √754 falls somewhere between 27 and 28.
Step 2: Now we need to apply the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). Going by the formula (754 - 729) ÷ (784 - 729) ≈ 0.459.
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 27 + 0.459 ≈ 27.459, so the square root of 754 is approximately 27.459.
Common Mistakes and How to Avoid Them in the Square Root of 754
Students do make mistakes while finding the square root, like forgetting about the negative square root and 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 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 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 ≈ 7.071.
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 at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 754 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √754?
The area of the square is 754 square units.
Explanation
The area of the square = side².
The side length is given as √754.
Area of the square = side² = √754 x √754 = 754.
Therefore, the area of the square box is 754 square units.
Problem 2
A square-shaped building measuring 754 square feet is built; if each of the sides is √754, what will be the square feet of half of the building?
377 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 754 by 2 = 377.
So half of the building measures 377 square feet.
Problem 3
Calculate √754 x 5.
Approximately 137.295
Explanation
The first step is to find the square root of 754, which is approximately 27.459.
The second step is to multiply 27.459 with 5.
So 27.459 x 5 ≈ 137.295.
Problem 4
What will be the square root of (754 + 46)?
The square root is 28.
Explanation
To find the square root, we need to find the sum of (754 + 46). 754 + 46 = 800, and then √800 ≈ 28.28.
Therefore, the square root of (754 + 46) is approximately ±28.28.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √754 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 130.918 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√754 + 38) ≈ 2 × (27.459 + 38) = 2 × 65.459 = 130.918 units.
FAQ on Square Root of 754
1.What is √754 in its simplest form?
2.Mention the factors of 754.
3.Calculate the square of 754.
4.Is 754 a prime number?
5.754 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 754?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 754?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 754
- Square root: A square root is the inverse of a square. Example: 4² = 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.
- Long division method: A step-by-step division process used to calculate square roots for non-perfect squares.
- Approximation method: A method used to estimate the square root of non-perfect squares by using nearby perfect squares.
- Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4².
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Jaskaran Singh Saluja
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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.
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