Square Root of 2720

The square root is the inverse of the square of the number. 2720 is not a perfect square. The square root of 2720 is expressed in both radical and exponential form. In radical form, it is expressed as √2720, whereas (2720)^(1/2) in exponential form. √2720 ≈ 52.1536, 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 2720 is broken down into its prime factors.

Step 1: Finding the prime factors of 2720 Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 17: 2^4 x 5 x 17

Step 2: Now we found the prime factors of 2720. The second step is to make pairs of those prime factors.

Since 2720 is not a perfect square, the digits of the number can’t be grouped into pairs.

Therefore, calculating 2720 using prime factorization is impossible.

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 2720, we need to group it as 20 and 27.

Step 2: Now we need to find n whose square is ≤ 27. We can say n is '5' because 5 x 5 = 25, which is lesser than 27. Now the quotient is 5, and after subtracting 25 from 27, the remainder is 2.

Step 3: Now let us bring down 20, which is the new dividend. Add the old divisor with the same number: 5 + 5 = 10, which will be our new divisor.

Step 4: We get 10n as the new divisor. We need to find the value of n.

Step 5: The next step is finding 10n x n ≤ 220. Let us consider n as 2, now 10 x 2 x 2 = 200.

Step 6: Subtract 200 from 220, the difference is 20, and the quotient is 52.

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 2000.

Step 8: Now we need to find the new divisor, which is 104, because 104 x 9 = 936.

Step 9: Subtracting 936 from 2000 gives the result of 1064.

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

So the square root of √2720 is approximately 52.15.

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 2720 using the approximation method.

Step 1: Now we have to find the closest perfect squares of √2720. The smallest perfect square less than 2720 is 2704 (52^2), and the largest perfect square greater than 2720 is 2809 (53^2). √2720 falls somewhere between 52 and 53.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (2720 - 2704) / (2809 - 2704) = 16 / 105 ≈ 0.1524. 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 52 + 0.1524 ≈ 52.15.

So the square root of 2720 is approximately 52.15.

• 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 has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
   
• Prime factorization: Prime factorization is the process of breaking down a number into its basic building blocks, which are prime numbers.
   
• Long division method: The long division method is a step-by-step process used to find the square root of a non-perfect square, which involves dividing the number into groups and calculating the square root iteratively.