Square Root of 841

The square root is the inverse of the square of the number. 841 is a perfect square. The square root of 841 is expressed in both radical and exponential form. In the radical form, it is expressed as √841, whereas (841)^(1/2) in the exponential form. √841 = 29, 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 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 841 is broken down into its prime factors.

Step 1: Finding the prime factors of 841 Breaking it down, we get 29 x 29: 29^2

Step 2: Now we found out the prime factors of 841. The second step is to make pairs of those prime factors. Since 841 is a perfect square, we can group the digits in pairs and find the square root.

Therefore, √841 = 29.

The long division method can be used for both perfect and non-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 pair the numbers from right to left. In the case of 841, we need to pair it as 8 and 41.

Step 2: Now we need to find n whose square is less than or equal to 8. We can take n as ‘2’ because 2 x 2 = 4, which is less than 8. Now the quotient is 2, and after subtracting 4 from 8, the remainder is 4.

Step 3: Bring down 41, making the new dividend 441. Add the old divisor with the same number 2 + 2 = 4, which will be our new divisor.

Step 4: The new divisor will be written as 4n. We need to find the value of n.

Step 5: The next step is finding 4n x n ≤ 441. Let us consider n as 9, now 49 x 9 = 441

Step 6: Subtract 441 from 441, and the remainder is 0, with the quotient as 29.

So the square root of √841 is 29.

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 approximate the square root of 841.

Step 1: We need to find the closest perfect squares around √841. The perfect squares closest to 841 are 784 (28^2) and 900 (30^2). √841 falls exactly between 28 and 30.

Step 2: Since 841 is a perfect square, we know that √841 = 29 exactly. Therefore, the square root of 841 is 29.

• Square root: A square root is the inverse operation of squaring a number. Example: 4^2 = 16, and the inverse operation is the square root, so √16 = 4.

• Rational number: A rational number is a number that can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

• Perfect square: A perfect square is a number that is the square of an integer. Example: 841 is a perfect square because it is 29^2.

• Long division method: A method used to find the square root of a number by dividing the number into pairs of digits from right to left.

• Approximation method: An approach to find an approximate value of the square root by identifying two consecutive integers between which the square root lies.