Square Root of 1764

The square root is the inverse of the square of the number. 1764 is a perfect square. The square root of 1764 is expressed in both radical and exponential form. In the radical form, it is expressed as √1764, whereas (1764)^(1/2) in the exponential form. √1764 = 42, which is a rational number because it can 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. 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 1764 is broken down into its prime factors.

Step 1: Finding the prime factors of 1764 Breaking it down, we get 2 x 2 x 3 x 3 x 7 x 7: 2^2 x 3^2 x 7^2

Step 2: Now we found out the prime factors of 1764. The second step is to make pairs of those prime factors. Since 1764 is a perfect square, we can group the digits of the number in pairs.

Therefore, calculating the square root of 1764 using prime factorization is possible. The square root is 2 x 3 x 7 = 42.

The long division method is particularly used for 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 1764, we need to group it as 64 and 17.

Step 2: Now we need to find n whose square is less than or equal to 17. We can choose n as 4 because 4 x 4 = 16 is less than 17. Now the quotient is 4, and after subtracting, the remainder is 1.

Step 3: Bring down 64, making the new dividend 164. Add the old divisor with the same number, 4 + 4, to get 8, which will be our new divisor.

Step 4: The new divisor will be 8n. We need to find the value of n such that 8n x n ≤ 164. Let us consider n as 2, now 82 x 2 = 164.

Step 5: Subtract 164 from 164, and the remainder is 0. The quotient is 42.

Therefore, the square root of 1764 is 42.

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 1764 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1764. The smallest perfect square before 1764 is 1600, and the largest perfect square is 1764. √1764 is exactly 42.

Step 2: Since 1764 is a perfect square, no further approximation is needed.

The square root of 1764 is 42.

• Square root: A square root is the inverse of a square. Example: 6^2 = 36 and the inverse of the square is the square root, that is √36 = 6.

• Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.

• Perfect square: A perfect square is a number that is the square of an integer. Example: 49 is a perfect square because it is 7^2.

• Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors.

• Dividend: A dividend is a number that is being divided by another number in a division operation.