Square Root of 2601

The square root is the inverse of the square of the number. 2601 is a perfect square. The square root of 2601 is expressed in both radical and exponential form. In the radical form, it is expressed as √2601, whereas (2601)^(1/2) in the exponential form. √2601 = 51, 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 used for perfect square numbers. Since 2601 is a perfect square, it can be solved using the prime factorization method. However, other methods such as the long division method can also be used for verification. 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 2601 is broken down into its prime factors: Step 1: Finding the prime factors of 2601. Breaking it down, we get 3 × 3 × 17 × 17: 3² × 17². Step 2: Now we found out the prime factors of 2601. The second step is to make pairs of those prime factors. Since 2601 is a perfect square, the digits of the number can be grouped in pairs. Therefore, the square root of 2601 = 3 × 17 = 51.

The long division method can also be used for 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 2601, we need to group it as 26 and 01.

Step 2: Now we need to find n whose square is less than or equal to the first group, 26. We can say n is 5 because 5 × 5 = 25, which is less than 26. Now the quotient is 5, and after subtracting 25 from 26, the remainder is 1.

Step 3: Now let us bring down 01, making the new dividend 101. Add the old divisor (5) with the same number, 5 + 5, which gives us 10, the new divisor.

Step 4: The next step is finding n such that 10n × n ≤ 101. Let us consider n as 1, now 101 × 1 = 101. Step 5: Subtracting 101 from 101, the result is 0, and the quotient is 51.

Since there are no more digits to bring down, the square root of 2601 is thus determined to be 51.

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 2601 using the approximation method:

Step 1: Identify the perfect squares nearest to 2601. The perfect square less than 2601 is 2500 (50²) and the perfect square greater than 2601 is 2704 (52²). Therefore, √2601 falls between 50 and 52.

Step 2: Calculate the approximate value between these perfect squares. Since 2601 is a perfect square, we already determined it is 51, making this step straightforward.

• Square root: A square root is the inverse of squaring a number. Example: 7² = 49, and the inverse of the square is the square root, so √49 = 7.
   
• 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. Example: 49 is a perfect square because it is 7².
   
• Multiplication: Multiplication is one of the four elementary mathematical operations of arithmetic; it is the process of combining equal groups. Example: 5 × 4 = 20.
   
• Prime factorization: Prime factorization is expressing a number as the product of its prime numbers. Example: The prime factorization of 18 is 2 × 3².