Square Root of 4624

The square root is the inverse of the square of the number. 4624 is a perfect square. The square root of 4624 is expressed in both radical and exponential form. In the radical form, it is expressed as √4624, whereas (4624)^(1/2) in the exponential form. √4624 = 68, 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. For non-perfect square numbers, methods like 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 4624 is broken down into its prime factors.

Step 1: Finding the prime factors of 4624

Breaking it down, we get 2 × 2 × 2 × 2 × 17 × 17: 2^4 × 17^2

Step 2: Now we found out the prime factors of 4624. The second step is to make pairs of those prime factors. Since 4624 is a perfect square, we can group the factors into pairs of 2^2 × 17. Therefore, the square root of 4624 using prime factorization is 2^2 × 17 = 68.

The long division method is particularly used for perfect and non-perfect square numbers. In this method, we find the square root using a step-by-step division approach.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 4624, we group it as 46 and 24.

Step 2: Now we need to find a number whose square is less than or equal to 46. We can use 6 because 6 × 6 = 36, which is less than 46. Now the quotient is 6.

Step 3: Subtract 36 from 46; the remainder is 10. Bring down the next pair of digits, 24, making the new dividend 1024.

Step 4: Double the quotient and write it as the new divisor with a blank digit next to it (12_).

Step 5: Find a digit to fill the blank such that when you multiply the new divisor by this digit, the product is less than or equal to 1024. The digit is 8, making the divisor 128.

Step 6: 128 × 8 = 1024; subtracting gives a remainder of 0.

So the square root of √4624 is 68.

The approximation method is another method for finding square roots and is an easy method to find the square root of a given number. Now let us learn how to find the square root of 4624 using the approximation method.

Step 1: Find numbers whose squares are close to 4624. The perfect squares closest to 4624 are 4624 itself. Since 4624 is a perfect square, the approximation method directly confirms the square root as 68.

• 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.

• 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 can be expressed as the square of an integer. For example, 4624 is a perfect square because it is 68^2.

• Exponent: An exponent refers to the number of times a number is multiplied by itself. For example, 2^3 = 2 × 2 × 2 = 8.

• Divisor: A divisor is a number by which another number is divided. For example, in 4624 ÷ 68 = 68, 68 is the divisor.