Square Root of 4840

The square root is the inverse of the square of the number. 4840 is not a perfect square. The square root of 4840 is expressed in both radical and exponential forms. In the radical form, it is expressed as √4840, whereas in the exponential form it is expressed as (4840)^(1/2). √4840 ≈ 69.535, 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 4840 is broken down into its prime factors.

Step 1: Finding the prime factors of 4840

Breaking it down, we get 2 × 2 × 2 × 5 × 11 × 11: 2^3 × 5^1 × 11^2

Step 2: Now we found out the prime factors of 4840. The second step is to make pairs of those prime factors. Since 4840 is not a perfect square, the digits of the number can’t be grouped in pairs perfectly. Therefore, calculating √4840 using prime factorization will only give an approximate value.

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 4840, we need to group it as 48 and 40.

Step 2: Now we need to find n whose square is less than or equal to 48. We can say n is ‘6’ because 6 × 6 = 36, which is less than or equal to 48. Now the quotient is 6. Subtracting 36 from 48, the remainder is 12.

Step 3: Bring down 40, which is the new dividend. Add the old divisor with the same number: 6 + 6 = 12, which will be our new divisor.

Step 4: The new divisor will be 12n. We need to find the value of n such that 12n × n is less than or equal to 1240. Let us consider n as 9: 129 × 9 = 1161.

Step 5: Subtracting 1161 from 1240 gives a remainder of 79.

Step 6: Since the dividend is less than the new 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 7900.

Step 7: Find the new divisor, which is 138. Continuing this process will yield the square root of 4840 as approximately 69.535.

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 4840 using the approximation method.

Step 1: We need to find the closest perfect squares to 4840. The smallest perfect square less than 4840 is 4761 (69^2), and the largest perfect square greater than 4840 is 4900 (70^2). √4840 falls somewhere between 69 and 70.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (4840 - 4761) / (4900 - 4761) ≈ 0.535 Using the formula, we identified the decimal point of our square root. The next step is adding the initial integer value to the decimal number: 69 + 0.535 = 69.535, so the square root of 4840 is approximately 69.535.

• 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.

• Long division method: A technique used to find the square root of a number by dividing and averaging iteratively.

• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.