115 LearnersLast updated on May 26th, 2025
Square Root of 1344
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1344.
What is the Square Root of 1344?
The square root is the inverse of the square of the number. 1344 is not a perfect square. The square root of 1344 is expressed in both radical and exponential form. In the radical form, it is expressed as √1344, whereas (1344)^(1/2) in the exponential form. √1344 = 36.66258, 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 1344
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 1344 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1344 is broken down into its prime factors.
Step 1: Finding the prime factors of 1344
Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 3 x 7: 2^5 x 3^1 x 7^1
Step 2: Now we have found the prime factors of 1344. The second step is to make pairs of those prime factors. Since 1344 is not a perfect square, the digits of the number can’t be grouped in pairs completely. Therefore, calculating √1344 using prime factorization is only an approximation.
Square Root of 1344 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 1344, we need to group it as 44 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 3^2 = 9, which is less than 13. Now the quotient is 3, and after subtracting 9 from 13, the remainder is 4.
Step 3: Now let us bring down 44, which is the new dividend. Add the old divisor with the same number, 3 + 3, to get 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding such n that 6n × n ≤ 444. Let us consider n as 7, now 67 × 7 = 469.
Step 6: Since 469 is greater than 444, we try n as 6. Now 66 × 6 = 396.
Step 7: Subtract 396 from 444, the difference is 48, and the quotient is 36.
Step 8: 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 4800.
Step 9: We find the new divisor as 732 because 732 × 6 = 4392.
Step 10: Subtracting 4392 from 4800, we get the result 408.
Step 11: Now the quotient is 36.6. Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.
So the square root of √1344 is approximately 36.66.
Square Root of 1344 by Approximation Method
The approximation method is another method for finding square roots, which is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1344 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √1344. The smallest perfect square less than 1344 is 1296 (36^2), and the largest perfect square greater than 1344 is 1369 (37^2). √1344 falls somewhere between 36 and 37.
Step 2: Now we need to apply the formula (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Using the formula (1344 - 1296) ÷ (1369 - 1296) = 0.66 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 36 + 0.66 = 36.66, so the square root of 1344 is approximately 36.66.
Common Mistakes and How to Avoid Them in the Square Root of 1344
Students often 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 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 has both positive and negative square roots. However, we typically consider only the positive square root, as it is the required one in many practical situations.
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 symbol 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 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 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; 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, resulting in a wrong answer at the end of the sum. This may happen in subtraction or elsewhere.
Square Root of 1344 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1344?
The area of the square is 1344 square units.
Explanation
The area of the square = side^2.
The side length is given as √1344.
Area of the square = side^2 = √1344 × √1344 = 1344.
Therefore, the area of the square box is 1344 square units.
Problem 2
A square-shaped building measuring 1344 square feet is built. If each of the sides is √1344, what will be the square feet of half of the building?
672 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped. Dividing 1344 by 2, we get 672. So half of the building measures 672 square feet.
Problem 3
Calculate √1344 × 5.
183.31
Explanation
The first step is to find the square root of 1344, which is approximately 36.66.
The second step is to multiply 36.66 by 5.
So, 36.66 × 5 = 183.31.
Problem 4
What will be the square root of (1300 + 44)?
The square root is approximately 36.66.
Explanation
To find the square root, we need to find the sum of (1300 + 44). 1300 + 44 = 1344, and √1344 ≈ 36.66.
Therefore, the square root of (1300 + 44) is approximately ±36.66.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1344 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 149.32 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1344 + 38) = 2 × (36.66 + 38) = 2 × 74.66 = 149.32 units.
FAQ on Square Root of 1344
1.What is √1344 in its simplest form?
2.Mention the factors of 1344.
3.Calculate the square of 1344.
4.Is 1344 a prime number?
5.1344 is divisible by?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 1344?
8.How do technology and digital tools in India support learning Algebra and Square Root of 1344?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 1344
- 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.
- Prime factorization: The process of expressing a number as the product of its prime factors. Example: The prime factorization of 1344 is 2^5 × 3 × 7.
- 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.
- Long division method: A method used to find the square root of non-perfect squares by dividing the number step-by-step.
- Approximation method: A method used to estimate the square root of a number by comparing it to the nearest perfect squares.
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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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