Square Root of 3136

The square root is the inverse of the square of the number. 3136 is a perfect square. The square root of 3136 is expressed in both radical and exponential form. In the radical form, it is expressed as √3136, whereas (3136)^(1/2) in the exponential form. √3136 = 56, 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 can be used for perfect square numbers. For non-perfect square numbers, methods like long-division and approximation are used. Let us now learn the following methods for finding the square root of 3136:

• Prime factorization method
   
• Long division method

The product of prime factors is the prime factorization of a number. Now let us look at how 3136 is broken down into its prime factors.

Step 1: Finding the prime factors of 3136 Breaking it down, we get 2 x 2 x 2 x 2 x 7 x 7: 2^4 x 7^2

Step 2: Now we found the prime factors of 3136. The second step is to make pairs of those prime factors. Since 3136 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating 3136 using prime factorization is possible.

Step 3: Taking one number from each pair gives us 2^2 x 7 = 4 x 7 = 28 Thus, the square root of 3136 is 56.

The long division method is used to find the square root of perfect square numbers too. 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 3136, we need to group it as 36 and 31.

Step 2: Now we need to find n whose square is less than or equal to 31. We can say n as '5' because 5^2 = 25 is less than 31. Now the quotient is 5; after subtracting 25 from 31, the remainder is 6.

Step 3: Now let us bring down 36, which is the new dividend. Add the old divisor with the same number: 5 + 5 = 10, which will be our new divisor.

Step 4: The new divisor will be 10n. We need to find the value of n such that 10n x n ≤ 636. Let's consider n as 6; now 106 x 6 = 636.

Step 5: Subtract 636 from 636; the difference is 0, and the quotient is 56. So the square root of √3136 is 56.

The approximation method is not necessary for perfect squares but can be applied to understand the proximity of results. For 3136, direct methods are more efficient.

• Square root: A square root is the inverse of a square. For example, 7^2 = 49, and the inverse of the square is the square root, that is, √49 = 7.

• Rational number: A rational number is a number that can be expressed 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. For example, 36 is a perfect square because it is 6^2.

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

• Divisor: A divisor is a number that divides another number completely without leaving a remainder. For instance, 7 is a divisor of 49.