Square Root of 1372

The square root is the inverse of the square of the number. 1372 is not a perfect square. The square root of 1372 is expressed in both radical and exponential form. In the radical form, it is expressed as √1372, whereas (1372)^(1/2) in the exponential form. √1372 ≈ 37.041, 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, for non-perfect square numbers, 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 1372 is broken down into its prime factors.

Step 1: Finding the prime factors of 1372.

Breaking it down, we get 2 x 2 x 343: 2^2 x 7^3.

Step 2: Now we have found the prime factors of 1372. The second step is to make pairs of those prime factors. Since 1372 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 1372 using prime factorization is not straightforward.

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 1372, we can group it as 13 and 72.

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 is lesser than 13. Now the quotient is 3 after subtracting 13 - 9, and the remainder is 4.

Step 3: Now let us bring down 72, making the new dividend 472. Add the old divisor with the same number, 3 + 3, we get 6, which will be our new divisor.

Step 4: We need to find a number such that 6n x n ≤ 472. Let us consider n as 7, as 67 x 7 = 469.

Step 5: Subtract 469 from 472, and the difference is 3.

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 zeroes to the dividend. Now the new dividend is 300.

Step 7: The new divisor is 74, because 740 x 4 = 296.

Step 8: Subtracting 296 from 300, we get the remainder 4.

Step 9: Continue doing these steps until we get two numbers after the decimal point.

The quotient is approximately 37.04.

The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Let us learn how to find the square root of 1372 using the approximation method.

Step 1: Now we have to find the closest perfect squares to √1372. The smallest perfect square less than 1372 is 1369, and the largest perfect square greater than 1372 is 1444. √1372 falls somewhere between 37 and 38.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1372 - 1369) / (1444 - 1369) = 3 / 75 = 0.04. The square root of 1372 is approximately 37 + 0.04 = 37.04.

• Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, since 4 x 4 = 16.

• Irrational number: An irrational number is a number that cannot be written as a simple fraction - that is, it cannot be expressed as a ratio of two integers.

• Principal square root: A number has both positive and negative square roots. The principal square root is the non-negative square root of a number.

• Prime factorization: Breaking down a composite number into its prime factors. For example, the prime factorization of 1372 is 2 x 2 x 7 x 7 x 7.

• Decimal: A decimal is a number that consists of a whole number and a fractional part separated by a decimal point. For example, 37.041 is a decimal number.