137 LearnersLast updated on May 26th, 2025
Square Root of 745
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 745.
What is the Square Root of 745?
The square root is the inverse of the square of the number. 745 is not a perfect square. The square root of 745 is expressed in both radical and exponential form. In the radical form, it is expressed as √745, whereas 745^(1/2) in the exponential form. √745 ≈ 27.288, 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 745
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 745 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 745 is broken down into its prime factors.
Step 1: Finding the prime factors of 745 Breaking it down, we get 5 x 149: 5¹ x 149¹
Step 2: Now we found out the prime factors of 745. Since 745 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 745 using prime factorization is not feasible for finding its square root.
Square Root of 745 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 745, we need to group it as 45 and 7.
Step 2: Now we need to find n whose square is less than or equal to 7. We can say n as ‘2’ because 2 x 2 = 4, which is less than 7. Now the quotient is 2; after subtracting 4 from 7, the remainder is 3.
Step 3: Now let us bring down 45, making the new dividend 345. Add the old divisor with the same number, 2 + 2, we get 4, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 4n x n ≤ 345. Let us consider n as 7, now 47 x 7 = 329.
Step 6: Subtract 329 from 345; the difference is 16, and the quotient is 27.
Step 7: 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 1600.
Step 8: Now we need to find the new divisor that is 547 because 547 x 2 = 1094.
Step 9: Subtracting 1094 from 1600, we get the result 506.
Step 10: Now the quotient becomes 27.2.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.
So the square root of √745 ≈ 27.288.
Square Root of 745 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 745 using the approximation method.
Step 1: We need to find the closest perfect squares around 745.
The smallest perfect square less than 745 is 729, and the largest perfect square greater than 745 is 784. √745 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 the formula, (745 - 729) / (784 - 729) = 16 / 55 ≈ 0.291. 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 + 0.291 ≈ 27.291.
So the square root of 745 is approximately 27.291.
Common Mistakes and How to Avoid Them in the Square Root of 745
Students do make mistakes while finding the square root, such as 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 typically focus on the principal (positive) square root, as it is the required one.
For example: √745 ≈ 27.288, but there is also -27.288 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 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 either happen in subtracting or elsewhere.
Square Root of 745 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √745?
The area of the square is approximately 745 square units.
Explanation
The area of the square = side^2.
The side length is given as √745.
Area of the square = side^2 = √745 x √745 = 745.
Therefore, the area of the square box is approximately 745 square units.
Problem 2
A square-shaped building measuring 745 square feet is built; if each of the sides is √745, what will be the square feet of half of the building?
372.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 745 by 2, we get 372.5.
So half of the building measures 372.5 square feet.
Problem 3
Calculate √745 x 5.
Approximately 136.44
Explanation
The first step is to find the square root of 745, which is approximately 27.288, the second step is to multiply 27.288 by 5.
So 27.288 x 5 ≈ 136.44.
Problem 4
What will be the square root of (745 + 4)?
The square root is approximately 27.495
Explanation
To find the square root, we need to find the sum of (745 + 4). 745 + 4 = 749, and then √749 ≈ 27.495.
Therefore, the square root of (745 + 4) is approximately 27.495.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √745 units and the width ‘w’ is 20 units.
The perimeter of the rectangle is approximately 94.576 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√745 + 20) = 2 × (27.288 + 20) = 2 × 47.288 ≈ 94.576 units.
FAQ on Square Root of 745
1.What is √745 in its simplest form?
2.Mention the factors of 745.
3.Calculate the square of 745.
4.Is 745 a prime number?
5.745 is divisible by?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 745?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 745?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 745
- 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.
- Principal square root: A number has both positive and negative square roots; however, the positive square root is more prominent due to its uses in the real world. This is known as the principal square root.
- Integer: Integers are a combination of whole numbers and their negatives, for example, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, etc.
- Decimal: A decimal represents a number with a whole part and a fractional part, for example, 7.86, 8.65, and 9.42 are decimals.
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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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