Square Root of 676

The square root is the inverse of the square of the number. 676 is a perfect square. The square root of 676 is expressed in both radical and exponential form. In the radical form, it is expressed as √676, whereas (676)^(1/2) in the exponential form. √676 = 26, 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. However, for non-perfect square numbers, 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 676 is broken down into its prime factors.

Step 1: Finding the prime factors of 676 Breaking it down, we get 2 x 2 x 13 x 13: 2^2 x 13^2

Step 2: Now we found out the prime factors of 676. The second step is to make pairs of those prime factors. Since 676 is a perfect square, the digits of the number can be grouped in pairs.

Therefore, calculating √676 using prime factorization gives us 26.

The long division method is particularly used for non-perfect square numbers, but it can also verify perfect squares. 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 676, we need to group it as 76 and 6.

Step 2: Now we need to find n whose square is 6. We can say n as ‘2’ because 2 x 2 = 4 is lesser than 6. Now the quotient is 2, after subtracting 6 - 4, the remainder is 2.

Step 3: Now let us bring down 76, which is the new dividend. Add the old divisor with the same number 2 + 2, we get 4, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 4n × n ≤ 276. Let us consider n as 6, now 4 x 6 x 6 = 276.

Step 6: Subtract 276 from 276, the difference is 0, and the quotient is 26.

So the square root of √676 is 26.

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 676 using the approximation method.

Step 1: Now we have to find the closest perfect square of √676. Since 676 is a perfect square, it falls directly at 26.

Step 2: No further steps are needed as 676 is a perfect square, and its square root is already an integer.

• Square root: A square root is the inverse of a square. Example: 5² = 25, and the inverse of the square is the square root, which is √25 = 5.
   
• 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. For example, 676 is a perfect square because it is 26².
   
• Integer: An integer is a whole number that can be positive, negative, or zero. For example, -5, 0, and 3 are integers.
   
• Perimeter: The perimeter is the total distance around a two-dimensional shape.