Square Root of 1672

The square root is the inverse of the square of the number. 1672 is not a perfect square. The square root of 1672 is expressed in both radical and exponential form. In radical form, it is expressed as √1672, whereas (1672)^(1/2) in exponential form. √1672 ≈ 40.8855, 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's 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 1672 is broken down into its prime factors.

Step 1: Finding the prime factors of 1672. Breaking it down, we get 2 x 2 x 2 x 11 x 19. In exponential form, it's 2^3 x 11 x 19.

Step 2: Now we have found the prime factors of 1672. The second step is to make pairs of those prime factors. Since 1672 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating 1672 using prime factorization is not feasible.

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's 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 1672, we need to group it as 72 and 16.

Step 2: Now we need to find n whose square is closest to 16. Here, n is 4 because 4 x 4 = 16. The quotient is 4, and the remainder is 0 after subtracting 16 - 16.

Step 3: Now let’s bring down 72, which is the new dividend. Add the old divisor with the same number: 4 + 4 = 8, which will be our new divisor.

Step 4: The new divisor is 8n. We need to find the value of n.

Step 5: The next step is finding 8n × n ≤ 72. Let us consider n as 0, so 8 x 0 x 0 = 0.

Step 6: Since the dividend is greater 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 7200.

Step 7: Now we need to find the new divisor. We find n = 5 because 85 x 5 = 425.

Step 8: Subtracting 425 from 7200, we get the result 6775.

Step 9: Continue doing these steps until we get two numbers after the decimal point, or until the remainder is zero.

So the square root of √1672 ≈ 40.89.

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 1672 using the approximation method.

Step 1: Now we have to find the closest perfect squares to √1672.

The smallest perfect square less than 1672 is 1600, and the largest perfect square greater than 1672 is 1764.

√1672 falls somewhere between 40 and 42.

Step 2: Now we need to apply the formula:

(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).

Using the formula: (1672 - 1600) / (1764 - 1600) = 72 / 164 ≈ 0.439.

Adding this to the smaller integer root, we get 40 + 0.439 = 40.439, so the square root of 1672 is approximately 40.44.

• 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, 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, which is why it is also known as the principal square root.
   
• Prime factorization: The expression of a number as the product of its prime numbers.
   
• Decimal: If a number has a whole number and a fraction combined into a single number, it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.