Square Root of 4761

The square root is the inverse of the square of the number. 4761 is a perfect square. The square root of 4761 is expressed in both radical and exponential form. In the radical form, it is expressed as √4761, whereas (4761)^(1/2) in the exponential form. √4761 = 69, 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 4761 is a perfect square, we can use the prime factorization method to find its square root. Other methods, such as the long division method and approximation method, can also be 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 4761 is broken down into its prime factors:

Step 1: Finding the prime factors of 4761

Breaking it down, we get 3 x 3 x 23 x 23: 3² x 23²

Step 2: Now we found out the prime factors of 4761. The second step is to make pairs of those prime factors. Since 4761 is a perfect square, the digits of the number can be grouped into pairs. Therefore, √4761 = 3 x 23 = 69.

The long division method is particularly used for perfect and non-perfect square numbers. 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 4761, we need to group it as 47 and 61.

Step 2: Now we need to find n whose square is less than or equal to 47. We can say n is 6 because 6 x 6 = 36, which is less than 47. The quotient is 6, and the remainder is 47 - 36 = 11.

Step 3: Bring down 61 to make the new dividend 1161. Double the quotient (6) to get 12, which will be our new divisor.

Step 4: Find a digit m such that 12m x m is less than or equal to 1161. We find that m is 9 because 129 x 9 = 1161.

Step 5: Since there is no remainder, the quotient is 69. Therefore, the square root of 4761 is 69.

The approximation method can be used to confirm the square root of a number. Since 4761 is a perfect square, approximation will confirm the result:

Step 1: We know that 4761 is between 3600 (60²) and 4900 (70²). Therefore, √4761 falls between 60 and 70.

Step 2: Calculate the midpoint: (60 + 70) / 2 = 65. Test squares around this point. Step 3: We find that 69 x 69 = 4761, confirming that the square root of 4761 is 69.

• Square root: A square root is the inverse of a square. Example: 8² = 64, and the inverse of the square is the square root, that is √64 = 8.

• 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: 64 is a perfect square of 8.

• Prime factorization: The expression of a number as a product of its prime factors. Example: The prime factorization of 18 is 2 x 3 x 3.

• Integer: An integer is a whole number that can be positive, negative, or zero. Example: -2, 0, 3, 42 are integers.