Square Root of 4050

The square root is the inverse of the square of a number. 4050 is not a perfect square. The square root of 4050 is expressed in both radical and exponential form. In radical form, it is expressed as √4050, whereas (4050)^(1/2) in exponential form. √4050 ≈ 63.63961, 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 4050 is broken down into its prime factors.

Step 1: Finding the prime factors of 4050 Breaking it down, we get 2 x 3 x 3 x 3 x 5 x 5 x 9.

Step 2: We have found the prime factors of 4050. The second step is to make pairs of those prime factors. Since 4050 is not a perfect square, the digits of the number can’t be grouped into pairs completely.

Therefore, calculating √4050 using prime factorization alone is not possible.

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 4050, we need to group it as 50 and 40.

Step 2: Now we need to find n whose square is 40. We can say n as ‘6’ because 6 x 6 is lesser than or equal to 40. Now, the quotient is 6. After subtracting 36 (6 x 6) from 40, the remainder is 4.

Step 3: Bring down 50, making the new dividend 450. Add the old divisor with the same number, 6 + 6, to get 12, which will be our new divisor.

Step 4: We need to find n such that 12n x n ≤ 450. Let us consider n as 3, now 123 x 3 = 369.

Step 5: Subtract 369 from 450; the difference is 81, and the quotient now is 63.

Step 6: 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 8100.

Step 7: We need to find the new divisor, which is 636, because 636 x 1 = 636.

Step 8: Subtracting 636 from 8100, we get a remainder of 1740.

Step 9: The quotient is 63.6.

Step 10: Continue doing these steps until we get two numbers after the decimal point. If there is no decimal value, continue until the remainder is zero.

So the square root of √4050 is approximately 63.64.

The approximation method is another method for finding 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 4050 using the approximation method.

Step 1: We have to find the closest perfect squares to √4050. The smallest perfect square less than 4050 is 3969, and the largest perfect square greater than 4050 is 4225. √4050 falls somewhere between 63 and 65.

Step 2: Now, apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula (4050 - 3969) ÷ (4225 - 3969) = 81 ÷ 256 ≈ 0.316 Using the formula, we identify the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 63 + 0.316 = 63.316.

So the square root of 4050 is approximately 63.316.

• Square root: A square root is the inverse of a square. For 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 why it is known as the principal square root.
   
• Prime factorization: Prime factorization is expressing a number as the product of its prime factors.
   
• Long division method: A method used to divide large numbers by breaking down the division process into simpler steps. It is particularly useful for finding square roots of non-perfect squares.