127 LearnersLast updated on May 26th, 2025
Square Root of 789
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 789.
What is the Square Root of 789?
The square root is the inverse of the square of the number. 789 is not a perfect square. The square root of 789 is expressed in both radical and exponential form. In the radical form, it is expressed as √789, whereas (789)^(1/2) in the exponential form. √789 ≈ 28.089, 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 789
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 789 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 789 is broken down into its prime factors:
Step 1: Finding the prime factors of 789 Breaking it down, we get 3 × 263: 3^1 × 263^1
Step 2: Now we found out the prime factors of 789. The second step is to make pairs of those prime factors. Since 789 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.
Therefore, calculating √789 using prime factorization directly is not feasible.
Square Root of 789 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 789, we need to group it as 89 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 × 2 = 4, which 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 89, which is the new dividend. Add the old divisor with the same number 2 + 2 = 4, which will be our new divisor.
Step 4: The new divisor will be 4n, and we need to find the value of n such that 4n × n ≤ 389. Let n be 7, now 47 × 7 = 329.
Step 5: Subtract 329 from 389. The difference is 60, 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 zeros to the dividend. Now the new dividend is 6000.
Step 7: Now we need to find the new divisor that is 547 because 547 × 9 = 4923.
Step 8: Subtracting 4923 from 6000 gives the result 1077.
Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values, continue till the remainder is zero.
So the square root of √789 is approximately 28.08.
Square Root of 789 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 789 using the approximation method.
Step 1: Now we have to find the closest perfect square of √789.
The smallest perfect square less than 789 is 784, and the largest perfect square greater than 789 is 841. √789 falls somewhere between 28 and 29.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (789 - 784) / (841 - 784) = 5 / 57 ≈ 0.088.
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 28 + 0.088 = 28.088, so the square root of 789 is approximately 28.088.
Common Mistakes and How to Avoid Them in the Square Root of 789
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping the long division method. 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 often take only the positive square root, as it is the required one.
For example, √50 = 7.07, but 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 students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving on to the next step.
For example, √(12+24) ≠ √12 + √24. The correct way 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 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; 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 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 calculation. This may either happen in subtracting or elsewhere.
Square Root of 789 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √789?
The area of the square is approximately 789 square units.
Explanation
The area of the square = side².
The side length is given as √789.
Area of the square = side² = √789 × √789 = 789.
Therefore, the area of the square box is approximately 789 square units.
Problem 2
A square-shaped building measuring 789 square feet is built; if each of the sides is √789, what will be the square feet of half of the building?
394.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 789 by 2 = 394.5
So half of the building measures 394.5 square feet.
Problem 3
Calculate √789 × 5.
Approximately 140.445
Explanation
The first step is to find the square root of 789, which is approximately 28.089.
The second step is to multiply 28.089 by 5.
So 28.089 × 5 ≈ 140.445
Problem 4
What will be the square root of (789 + 11)?
The square root is 28
Explanation
To find the square root, we need to find the sum of (789 + 11). 789 + 11 = 800, and then √800 ≈ 28.28.
Therefore, the square root of (789 + 11) is approximately 28.28.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √789 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 132.178 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√789 + 38) = 2 × (28.089 + 38) = 2 × 66.089 = 132.178 units.
FAQ on Square Root of 789
1.What is √789 in its simplest form?
2.Mention the factors of 789.
3.Calculate the square of 789.
4.Is 789 a prime number?
5.789 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 789?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 789?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 789
- 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.
- Approximation: The process of estimating a value based on nearby values, often used when exact values are not necessary or possible.
- Prime factorization: Expressing a number as the product of its prime numbers. Example: 789 = 3 × 263.
- Long division method: A step-by-step method used to find the square root of non-perfect squares by dividing the number into groups and calculating manually.
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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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