Square Root of 6050

The square root is the inverse of the square of the number. 6050 is not a perfect square. The square root of 6050 is expressed in both radical and exponential form. In the radical form, it is expressed as √6050, whereas (6050)^(1/2) in the exponential form. √6050 ≈ 77.7987, 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, the prime factorization method is not used for non-perfect square numbers where 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 6050 is broken down into its prime factors.

Step 1: Finding the prime factors of 6050 Breaking it down, we get 2 x 5 x 5 x 11 x 11: 2^1 x 5^2 x 11^2

Step 2: Now we found out the prime factors of 6050. The second step is to make pairs of those prime factors. Since 6050 is not a perfect square, the digits of the number can’t be grouped into perfect pairs.

Therefore, calculating 6050 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 6050, we need to group it as 50 and 60.

Step 2: Now we need to find n whose square is less than or equal to 60. We can say n as ‘7’ because 7 x 7 = 49 is less than 60. Now the quotient is 7, and after subtracting 49 from 60, the remainder is 11.

Step 3: Now let us bring down 50, which is the new dividend. Add the old divisor with the same number 7 + 7 to get 14, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 14n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 14n x n ≤ 1150. Let us consider n as 8, now 148 x 8 = 1184.

Step 6: Subtract 1150 from 1184, the difference is 34, and the quotient is 77.

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 3400.

Step 8: Now we need to find the new divisor that is 778 because 778 x 4 = 3112.

Step 9: Subtracting 3112 from 3400, we get the result 288.

Step 10: Now the quotient is 77.8.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.

So the square root of √6050 is approximately 77.80.

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 6050 using the approximation method.

Step 1: Now we have to find the closest perfect square of √6050.

The smallest perfect square of 6050 is 5776 and the largest perfect square of 6050 is 6084. √6050 falls somewhere between 76 and 78.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Going by the formula (6050 - 5776) ÷ (6084 - 5776) ≈ 0.7987.

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 77 + 0.7987 ≈ 77.80, so the square root of 6050 is approximately 77.80.

• 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, that 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 is more prominent due to its uses in the real world. That is the reason it is also known as the principal square root.

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

• 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.