Square Root of 8281

The square root is the inverse of the square of the number. 8281 is a perfect square. The square root of 8281 is expressed in both radical and exponential form. In the radical form, it is expressed as √8281, whereas (8281)^(1/2) in the exponential form. √8281 = 91, 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, the long division method and approximation method are used. Since 8281 is a perfect square, we will use the prime factorization method. 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 8281 is broken down into its prime factors.

Step 1: Finding the prime factors of 8281 Breaking it down, we get 91 x 91 = 8281. 91 is a product of 7 and 13, so the prime factorization of 8281 is 7 x 13 x 7 x 13.

Step 2: Now we found out the prime factors of 8281. The second step is to make pairs of those prime factors. Since 8281 is a perfect square, the digits of the number can be grouped in pairs. Therefore, √8281 = 7 x 13 = 91.

The long division method is another way to find the square root of a 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 8281, we group it as 82 and 81.

Step 2: Now we need to find n whose square is closest to 82. We can say n as '9' because 9 x 9 = 81, which is less than or equal to 82. Now the quotient is 9 after subtracting 81 from 82. The remainder is 1.

Step 3: Now let us bring down 81, making the new dividend 181. Add the old divisor with the same number 9 + 9 = 18, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 18n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 18n x n ≤ 181. Let us consider n as 1, now 18 x 1 x 1 = 18.

Step 6: Subtract 181 from 18, and the difference is 163. The quotient is 91.

Step 7: Since 8281 is a perfect square, continuing the steps will yield 0 as the remainder, confirming that the square root of 8281 is 91.

The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. However, since 8281 is a perfect square, we can directly determine that the square root is 91.

Square root: A square root is the inverse of a square. Example: 9^2 = 81, and the inverse of the square is the square root, which is √81 = 9.

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, 81 is a perfect square because it is 9^2. Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 28 is 2 x 2 x 7. Integer: An integer is a whole number that can be positive, negative, or zero. Examples include -3, 0, and 4.