101 LearnersLast updated on May 26th, 2025
Square Root of 1385
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 1385.
What is the Square Root of 1385?
The square root is the inverse of the square of a number. 1385 is not a perfect square. The square root of 1385 is expressed in both radical and exponential form. In the radical form, it is expressed as √1385, whereas (1385)^(1/2) in the exponential form. √1385 ≈ 37.204, 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 1385
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the 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 1385 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1385 is broken down into its prime factors:
Step 1: Finding the prime factors of 1385
Breaking it down, we get 5 x 277: 5^1 x 277^1
Step 2: Now we found out the prime factors of 1385. The second step is to make pairs of those prime factors. Since 1385 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 1385 using prime factorization is not feasible for finding an exact square root.
Square Root of 1385 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 1385, we need to group it as 85 and 13.
Step 2: Now we need to find n whose square is less than or equal to 13. We can say n is '3' because 3 x 3 = 9, which is less than 13. Now the quotient is 3, and after subtracting 9 from 13, the remainder is 4.
Step 3: Bring down 85 to make the new dividend 485. Add the old divisor 3 with itself to get 6, which will be our new divisor.
Step 4: Now we get 6n as the new divisor, we need to find the value of n.
Step 5: Find 6n x n ≤ 485. Let us consider n as 7, so 67 x 7 = 469.
Step 6: Subtract 469 from 485, the remainder is 16, and the quotient is 37.
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 zeroes to the dividend. Now the new dividend is 1600.
Step 8: Now we need to find the new divisor, which is 744 because 744 x 2 = 1488.
Step 9: Subtracting 1488 from 1600, we get the result 112.
Step 10: Now the quotient is 37.2.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Continue until the remainder is zero or sufficiently small.
So the square root of √1385 is approximately 37.20.
Square Root of 1385 by Approximation Method
The approximation method is another method for finding 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 1385 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √1385. The closest smaller perfect square to 1385 is 1369, and the closest larger perfect square is 1444. √1385 falls somewhere between 37 and 38.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula: (1385 - 1369) / (1444 - 1369) = 16/75 ≈ 0.213 Add this to the lower estimate: 37 + 0.213 = 37.213.
So the approximate square root of 1385 is 37.213.
Common Mistakes and How to Avoid Them in the Square Root of 1385
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 will be taking 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.
Square Root of 1385 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1385?
The area of the square is approximately 1920.64 square units.
Explanation
The area of the square = side².
The side length is given as √1385.
Area of the square = side² = √1385 x √1385 ≈ 37.204 x 37.204 ≈ 1385.
Therefore, the area of the square box is approximately 1385 square units.
Problem 2
A square-shaped building measuring 1385 square feet is built; if each of the sides is √1385, what will be the square feet of half of the building?
Approximately 692.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1385 by 2 = we get 692.5 So half of the building measures approximately 692.5 square feet.
Problem 3
Calculate √1385 x 5.
Approximately 186.02
Explanation
The first step is to find the square root of 1385, which is approximately 37.204.
The second step is to multiply 37.204 by 5.
So 37.204 x 5 ≈ 186.02.
Problem 4
What will be the square root of (1385 + 15)?
The square root is approximately 37.54
Explanation
To find the square root, we need to find the sum of (1385 + 15). 1385 + 15 = 1400, and then √1400 ≈ 37.42.
Therefore, the square root of (1385 + 15) is approximately ±37.42.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1385 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle is approximately 150.41 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1385 + 38) = 2 × (37.204 + 38) = 2 × 75.204 ≈ 150.41 units.
FAQ on Square Root of 1385
1.What is √1385 in its simplest form?
2.Mention the factors of 1385.
3.Calculate the square of 1385.
4.Is 1385 a prime number?
5.1385 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 1385?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 1385?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 1385
- Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, which 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, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
- Prime factorization: The representation of a number as a product of its prime factors. For example, the prime factorization of 1385 is 5 x 277.
- Long division method: A technique used to find the square root of non-perfect square numbers by dividing the number into smaller parts to find an approximation of the square root.
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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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