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.

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

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.

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.

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.

• 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.