Square Root of 2450

The square root is the inverse of the square of the number. 2450 is not a perfect square. The square root of 2450 is expressed in both radical and exponential form. In the radical form, it is expressed as √2450, whereas (2450)^(1/2) in the exponential form. √2450 ≈ 49.4975, 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 2450 is broken down into its prime factors.

Step 1: Finding the prime factors of 2450 Breaking it down, we get 2 x 5 x 5 x 7 x 7: 2^1 x 5^2 x 7^2

Step 2: Now we found out the prime factors of 2450. The second step is to make pairs of those prime factors. Since 2450 is not a perfect square, therefore the digits of the number can’t be grouped into perfect pairs for all factors. However, we can simplify it to 5 x 7 √2 or 35√2.

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 2450, we need to group it as 50 and 24.

Step 2: Now we need to find n whose square is less than or equal to 24. We can say n is ‘4’ because 4 x 4 = 16 is less than 24. Now the quotient is 4 after subtracting 24 - 16, the remainder is 8.

Step 3: Now let us bring down 50 which is the new dividend. 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 in the form of 8n. We need to find the value of n such that 8n x n ≤ 850. Let us consider n as 9, now 89 x 9 = 801.

Step 5: Subtract 850 from 801, the difference is 49, and the quotient is 49.

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 4900.

Step 7: Now we need to find the new divisor. Let’s try 495, because 495 x 9 = 4455.

Step 8: Subtracting 4455 from 4900 gives us 445.

Step 9: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √2450 is approximately 49.50.

The approximation method is another method for finding square roots, and 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 2450 using the approximation method.

Step 1: Now we have to find the closest perfect squares of √2450. The smallest perfect square less than 2450 is 2401 (49^2) and the largest perfect square greater than 2450 is 2500 (50^2). √2450 falls somewhere between 49 and 50.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).

Using the formula (2450 - 2401) ÷ (2500 - 2401) = 49 / 99 ≈ 0.4949. 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 49 + 0.4949 ≈ 49.50, so the square root of 2450 is approximately 49.50.

• 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.

• 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 has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.

• Approximation: The method of finding a value that is close enough to the right answer, usually within an acceptable range or tolerance.

• Prime factorization: Decomposing a composite number into a product of its prime factors.