Square Root of 7921

The square root is the inverse of the square of the number. 7921 is a perfect square. The square root of 7921 is expressed in both radical and exponential form. In radical form, it is expressed as √7921, whereas (7921)^(1/2) in exponential form. √7921 = 89, 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, other methods like 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 7921 is broken down into its prime factors.

Step 1: Finding the prime factors of 7921 Breaking it down, we get 89 x 89: 89²

Step 2: Now we have found the prime factors of 7921. The second step is to make pairs of those prime factors. Since 7921 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating 7921 using prime factorization gives us √7921 = 89.

The long division method is particularly used for both 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 7921, we group it as 79 and 21.

Step 2: Now we need to find n whose square is less than or equal to 79. We can say n as ‘8’ because 8 x 8 = 64 is less than 79. Now the quotient is 8, after subtracting 64 from 79 the remainder is 15.

Step 3: Let us bring down 21, making the new dividend 1521. Add the old divisor with the same number 8 + 8, we get 16 which will be our new divisor.

Step 4: The new divisor will be 16n. Now we need to find the value of n such that 16n x n ≤ 1521. Let us consider n as 9, now 169 x 9 = 1521.

Step 5: Subtract 1521 from 1521, the remainder is 0, and the quotient is 89. The square root of √7921 is 89.

The approximation method is another method for finding square roots, it is an easy method to find the square root of a given number. However, since 7921 is a perfect square, the approximation method is not necessary, as the exact answer is already known: √7921 = 89.

• Square root: A square root is the inverse of squaring a number. Example: 8² = 64, and the inverse of squaring 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. For example, 89² = 7921.
   
• Long division method: A method used to find square roots of both perfect and non-perfect squares by dividing the number into groups.
   
• Approximation method: A method used to find an approximate value of the square root of a non-perfect square when the exact value is not necessary.