Square Root of 4834

The square root is the inverse of the square of the number. 4834 is not a perfect square. The square root of 4834 is expressed in both radical and exponential forms. In the radical form, it is expressed as √4834, whereas (4834)^(1/2) in the exponential form. √4834 ≈ 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, for non-perfect square numbers, the prime factorization method is not used; instead, 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 4834 is broken down into its prime factors.

Step 1: Finding the prime factors of 4834. Breaking it down, we get 2 x 2417, but since 4834 is not a perfect square, it cannot be expressed by pairs of prime factors. Therefore, calculating 4834 using prime factorization is not feasible.

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 4834, we need to group it as 48 and 34.

Step 2: Now we need to find n whose square is less than or equal to 48. We can say n as '6' because 6 x 6 = 36, which is less than 48. The quotient is 6, and after subtracting 36 from 48, the remainder is 12.

Step 3: Now let us bring down 34, making the new dividend 1234. Add the old divisor with the same number, 6 + 6, to get 12, which becomes the new divisor.

Step 4: The new divisor is 12n, so we need to find the value of n.

Step 5: Find 12n x n ≤ 1234. Let us consider n as 9, now 129 x 9 = 1161.

Step 6: Subtract 1161 from 1234; the difference is 73, and the quotient is 69.

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 7300.

Step 8: Now we need to find the new divisor that is 139 because 1395 x 5 = 6975.

Step 9: Subtracting 6975 from 7300, we get the result 325.

Step 10: Now the quotient is 69.5

Step 11: Continue these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.

So the square root of √4834 ≈ 69.54

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 4834 using the approximation method.

Step 1: Now we have to find the closest perfect square to √4834. The perfect squares closest to 4834 are 4761 (69²) and 4900 (70²). √4834 falls somewhere between 69 and 70.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (4834 - 4761) / (4900 - 4761) = 73 / 139 ≈ 0.525 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 69 + 0.525 ≈ 69.525, so the square root of 4834 is approximately 69.525. 69 + 0.525 ≈ 69.525, so the square root of 4834 is approximately 69.525.

• Square root: A square root is the inverse of a square. Example: 4² = 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 the principal square root.

• Prime factorization: Prime factorization is finding which prime numbers multiply together to make the original number.

• Perfect square: A perfect square is a number that can be expressed as the product of an integer with itself. For example, 4, 9, 16, 25, etc., are perfect squares.