Square Root of 936

The square root is the inverse of the square of a number. 936 is not a perfect square. The square root of 936 is expressed in both radical and exponential form. In the radical form, it is expressed as √936, whereas in exponential form it is expressed as (936)^(1/2). √936 ≈ 30.594, 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 936 is broken down into its prime factors.

Step 1: Finding the prime factors of 936

Breaking it down, we get 2 x 2 x 2 x 3 x 3 x 13: 2^3 x 3^2 x 13

Step 2: Now we have found the prime factors of 936. The second step is to make pairs of those prime factors. Since 936 is not a perfect square, the digits of the number can’t be grouped into pairs.

Therefore, calculating 936 using prime factorization does not result in a perfect integer.

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 936, we need to group it as 36 and 9.

Step 2: Now we need to find n whose square is 9. We can say n as ‘3’ because 3 x 3 is lesser than or equal to 9. Now the quotient is 3, and after subtracting 9 from 9, the remainder is 0.

Step 3: Now let us bring down 36, 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, we need to find the value of n.

Step 5: The next step is finding 6n x n ≤ 36. Let us consider n as 5, now 6 x 5 x 5 = 30.

Step 6: Subtract 36 from 30; the difference is 6, and the quotient is 35.

Step 7: 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 600.

Step 8: Now we need to find the new divisor. Try 605 x 5 = 3025, which is too large, so try 604 x 4 = 2416.

Step 9: Subtracting 2416 from 6000 gives us the result 3584.

Step 10: Now the quotient is 30.5, and continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values, continue till the remainder is zero.

So the square root of √936 is approximately 30.594.

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 936 using the approximation method.

Step 1: Now we have to find the closest perfect square of √936.

The smallest perfect square less than 936 is 900 and the largest perfect square greater than 936 is 961.

√936 falls somewhere between 30 and 31.

Step 2: Now we need to apply the formula that is

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

Going by the formula (936 - 900) / (961 - 900) = 36 / 61 ≈ 0.5902.

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 30 + 0.5902 = 30.5902, so the square root of 936 is approximately 30.5902.

• Square root: A square root is the inverse of squaring a number. Example: 5^2 = 25 and the inverse of the square is the square root, that is √25 = 5.
   
• 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 is most commonly used in real-world applications, known as the principal square root.
   
• Prime factorization: Breaking down a number into prime numbers that multiply together to form the original number.
   
• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal, for example, 7.86, 8.65, and 9.42 are decimals.