Square Root of 5476

The square root is the inverse of the square of the number. 5476 is a perfect square. The square root of 5476 is expressed in both radical and exponential form. In the radical form, it is expressed as √5476, whereas (5476)^(1/2) in the exponential form. √5476 = 74, 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 can be used for perfect square numbers. For non-perfect squares, the long-division method and approximation method are used. Let us now learn the 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 5476 is broken down into its prime factors:

Step 1: Finding the prime factors of 5476 Breaking it down, we get 2 x 2 x 41 x 41: 2^2 x 41^2

Step 2: Now we found out the prime factors of 5476. The next step is to make pairs of those prime factors. Since 5476 is a perfect square, the digits of the number can be grouped in pairs.

Therefore, √5476 = 2 x 41 = 82.

The long division method is particularly used for 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 5476, we group it as 54 and 76.

Step 2: Now we need to find n whose square is less than or equal to 54. We can say n is 7 because 7 x 7 = 49, which is less than 54. The quotient is 7, and the remainder is 54 - 49 = 5.

Step 3: Bring down 76, making the new dividend 576. Add the old divisor with the same number 7 + 7 to get 14 as our new divisor.

Step 4: We need to find the value of n such that 14n x n ≤ 576. Let n be 4, then 144 x 4 = 576.

Step 5: Subtracting 576 - 576 gives a remainder of 0.

Step 6: The quotient is 74.

So the square root of √5476 is 74.

The approximation method is an easy method for finding the square roots. Here’s how to approximate the square root of 5476.

Step 1: Find the closest perfect square of √5476. The square root of 5476 is exactly 74, so the approximation method is not needed in this case since 5476 is a perfect square.

• Square root: A square root is the inverse of a square. Example: 8^2 = 64, and the inverse of the square is the square root, that is √64 = 8.

• Perfect square: A perfect square is a number that is the square of an integer. For example, 5476 is a perfect square because √5476 = 74.

• Rational number: A rational number can be expressed as the quotient or fraction p/q of two integers, where q is not zero.

• Integer: An integer is a whole number that can be positive, negative, or zero. For example, -3, 0, 2, 74 are integers.

• Factor: A factor is a number that divides another number without a remainder. For example, 2 is a factor of 4.