124 LearnersLast updated on May 26th, 2025
Square Root of 740
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 740.
What is the Square Root of 740?
The square root is the inverse of the square of the number. 740 is not a perfect square. The square root of 740 is expressed in both radical and exponential form. In the radical form, it is expressed as √740, whereas (740)^(1/2) in the exponential form. √740 ≈ 27.1928, 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 740
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 740 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 740 is broken down into its prime factors:
Step 1: Finding the prime factors of 740
Breaking it down, we get 2 x 2 x 5 x 37: 2^2 x 5 x 37
Step 2: Now we found out the prime factors of 740. The second step is to make pairs of those prime factors. Since 740 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 740 using prime factorization is impossible.
Square Root of 740 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 740, we need to group it as 40 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 is less than 7. Now the quotient is 2, and after subtracting 4 from 7, the remainder is 3.
Step 3: Now let us bring down 40, which is the new dividend. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor.
Step 4: The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 340. Let us consider n as 8; now 48 x 8 = 384, which is too high. Trying n as 7, we get 47 x 7 = 329, which fits.
Step 5: Subtract 329 from 340, the difference is 11, 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 1100.
Step 7: The new divisor becomes 547. We determine that n is 2 because 547 x 2 = 1094.
Step 8: Subtracting 1094 from 1100, we get the result 6.
Step 9: Now the quotient is 27.2
Step 10: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.
So the square root of √740 is approximately 27.1928.
Square Root of 740 by Approximation Method
The 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 740 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √740. The smallest perfect square less than 740 is 729, and the largest perfect square greater than 740 is 784. √740 falls somewhere between 27 and 28.
Step 2: Now we need to apply the formula (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using this, (740 - 729) ÷ (784 - 729) = 11 ÷ 55 ≈ 0.2 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 + 0.2 = 27.2, so the square root of 740 is approximately 27.2
Common Mistakes and How to Avoid Them in the Square Root of 740
Students do make mistakes while finding the square root, likewise forgetting about the negative square root, 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 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 ≈ 7.071067.
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 keep away from 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 happen in subtracting or elsewhere.
Square Root of 740 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √740?
The area of the square is approximately 547.2 square units.
Explanation
The area of the square = side^2.
The side length is given as √740.
Area of the square = side^2 = √740 x √740 ≈ 27.2 x 27.2 = 739.84
Therefore, the area of the square box is approximately 739.84 square units.
Problem 2
A square-shaped building measuring 740 square feet is built; if each of the sides is √740, what will be the square feet of half of the building?
370 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 740 by 2 = we get 370.
So half of the building measures 370 square feet.
Problem 3
Calculate √740 x 5.
135.96
Explanation
The first step is to find the square root of 740, which is approximately 27.1928, the second step is to multiply 27.1928 with 5. So 27.1928 x 5 ≈ 135.964
Problem 4
What will be the square root of (740 + 9)?
The square root is approximately 28.
Explanation
To find the square root, we need to find the sum of (740 + 9). 740 + 9 = 749, and then √749 ≈ 27.37.
Therefore, the square root of (740 + 9) is approximately 27.37.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √740 units and the width ‘w’ is 25 units.
We find the perimeter of the rectangle as approximately 104.39 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√740 + 25) ≈ 2 × (27.1928 + 25) ≈ 2 × 52.1928 ≈ 104.3856 units.
FAQ on Square Root of 740
1.What is √740 in its simplest form?
2.Mention the factors of 740.
3.Calculate the square of 740.
4.Is 740 a prime number?
5.740 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 740?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 740?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 740
- 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, 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.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 36 is a perfect square because it is 6^2.
- Decimal: If a number has a whole number and a fraction in a single number then it is called a decimal. Example: 7.86, 8.65, and 9.42 are decimals.
- Prime factorization: Prime factorization is expressing a number as the product of its prime factors. Example: The prime factorization of 28 is 2 x 2 x 7. ```
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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.
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