Square Root of 1225

The square root is the inverse of the square of the number. 1225 is a perfect square. The square root of 1225 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1225, whereas (1225)^(1/2) in the exponential form. √1225 = 35, 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 is typically used for perfect square numbers like 1225. The long division method and approximation method are more suited for non-perfect square numbers. Let us now learn the following method:

Prime factorization method

The product of prime factors is the prime factorization of a number. Now let us look at how 1225 is broken down into its prime factors.

Step 1: Finding the prime factors of 1225 Breaking it down, we get 5 x 5 x 7 x 7: 5^2 x 7^2 Step 2: Now we found out the prime factors of 1225. The second step is to make pairs of those prime factors. Since 1225 is a perfect square, the digits of the number can be grouped into pairs.

Therefore, calculating √1225 using prime factorization gives us 5 x 7 = 35.

The long division method is generally used for non-perfect square numbers but can be demonstrated for perfect squares like 1225 for practice. In this method, we verify that our calculation matches the known perfect square root.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 1225, we need to group it as 12 and 25.

Step 2: Now we need to find n whose square is less than or equal to 12. We can say n is ‘3’ because 3 x 3 = 9 is less than 12. Now the quotient is 3, and after subtracting 9 from 12, the remainder is 3.

Step 3: Now let us bring down 25, which is the new dividend. Add the old divisor with the same number, 3 + 3 = 6, which will be our new divisor.

Step 4: The next step is finding 6n x n ≤ 325. Let us consider n as 5; now 65 x 5 = 325.

Step 5: Subtract 325 from 325, and the remainder is 0. The quotient is 35.

Step 6: Since the remainder is 0, we can conclude that √1225 = 35.

The approximation method is not necessary for 1225 as it is a perfect square, but it can be used to verify the calculation.

Step 1: We find the closest perfect square to 1225, which are 1225 itself or nearby perfect squares.

Step 2: Since 1225 is a perfect square, √1225 directly gives us an integer value, which is 35.

• Square root: A square root is the inverse of a square. Example: 6^2 = 36, and the inverse of the square is the square root, that is √36 = 6.
   
• Rational number: A rational number is a number that can be written 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, 49, 64, etc.
   
• Prime factorization: Prime factorization is expressing a number as the product of its prime numbers.
   
• Integer: An integer is a whole number that can be positive, negative, or zero. Examples include -5, -4, 0, 1, 2, etc.