119 LearnersLast updated on May 26th, 2025
Square Root of 1394
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 1394.
What is the Square Root of 1394?
The square root is the inverse of the square of the number. 1394 is not a perfect square. The square root of 1394 is expressed in both radical and exponential form. In the radical form, it is expressed as √1394, whereas (1394)^(1/2) in the exponential form. √1394 ≈ 37.313, 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 1394
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 1394 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1394 is broken down into its prime factors.
Step 1: Finding the prime factors of 1394
Breaking it down, we get 2 x 19 x 73: 2^1 x 19^1 x 73^1
Step 2: Now we found out the prime factors of 1394. The second step is to make pairs of those prime factors. Since 1394 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 1394 using prime factorization does not yield a perfect square root.
Square Root of 1394 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 1394, we need to group it as 94 and 13.
Step 2: Now we need to find n whose square is 13. We can say n as ‘3’ because 3 x 3 = 9, which is less than 13. Now the quotient is 3; after subtracting 9 from 13, the remainder is 4.
Step 3: Now let us bring down 94, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the current quotient with the number we add in the next step. Now we look for a digit n such that 6n x n is less than or equal to 494.
Step 5: The next step is finding 6n x n ≤ 494. Let us consider n as 8, now 68 x 8 = 544, which is too high, so we try n as 7, then 67 x 7 = 469.
Step 6: Subtracting 469 from 494, the difference is 25, 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 2500.
Step 8: Now we need to find the new divisor that is 746 because 746 x 3 = 2238.
Step 9: Subtracting 2238 from 2500, we get the result 262.
Step 10: Now the quotient is 37.3
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 √1394 ≈ 37.313
Square Root of 1394 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 1394 using the approximation method.
Step 1: Now we find the closest perfect squares around √1394. The smallest perfect square less than 1394 is 1369, and the largest perfect square greater than 1394 is 1444. √1394 falls somewhere between 37 and 38.
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 (1394 - 1369) / (1444 - 1369) ≈ 0.333 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 37 + 0.333 ≈ 37.333.
So the square root of 1394 is approximately 37.313.
Common Mistakes and How to Avoid Them in the Square Root of 1394
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. 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: √1394 ≈ 37.313, there is also -37.313 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 either happen in subtracting or elsewhere.
Square root of 1394 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1394?
The area of the square is 1394 square units.
Explanation
The area of the square = side^2.
The side length is given as √1394.
Area of the square = side^2 = √1394 x √1394 = 1394.
Therefore, the area of the square box is 1394 square units.
Problem 2
A square-shaped building measuring 1394 square feet is built; if each of the sides is √1394, what will be the square feet of half of the building?
697 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1394 by 2 = we get 697.
So half of the building measures 697 square feet.
Problem 3
Calculate √1394 x 5.
186.565
Explanation
The first step is to find the square root of 1394, which is approximately 37.313.
The second step is to multiply 37.313 with 5.
So, 37.313 x 5 ≈ 186.565.
Problem 4
What will be the square root of (1376 + 18)?
The square root is 38.
Explanation
To find the square root, we need to find the sum of (1376 + 18). 1376 + 18 = 1394, and then √1394 ≈ 37.313.
Therefore, the square root of (1376 + 18) is approximately 37.313.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1394 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as 174.626 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1394 + 50) = 2 × (37.313 + 50) ≈ 2 × 87.313 = 174.626 units.
FAQ on Square Root of 1394
1.What is √1394 in its simplest form?
2.Mention the factors of 1394.
3.Calculate the square of 1394.
4.Is 1394 a prime number?
5.1394 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 1394?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 1394?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 1394
- 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, 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 a principal square root.
- Prime factorization: Breaking down a number into its basic prime number factors, which are the building blocks of the number.
- Long division method: A step-by-step process for dividing complex numbers to find square roots, especially useful for non-perfect squares. ```
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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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