Square Root of 941

The square root is the inverse of the square of the number. 941 is not a perfect square. The square root of 941 is expressed in both radical and exponential form. In the radical form, it is expressed as √941, whereas (941)^(1/2) in the exponential form. √941 ≈ 30.672, which is an irrational number because it cannot 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, the prime factorization method is not typically used for non-perfect square numbers, where the long-division method and approximation method are more applicable. Let us now learn the following methods:

1. Prime factorization method
2. Long division method
3. Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 941 is broken down into its prime factors.

Step 1: Finding the prime factors of 941 941 is a prime number, so its only prime factors are 1 and 941 itself.

Since 941 is not a perfect square, calculating the square root of 941 using prime factorization is impractical.

The long division method is particularly used for 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 group the numbers from right to left. In the case of 941, we group it as 41 and 9.

Step 2: Now we need to find n whose square is less than or equal to 9. We can say n is '3' because 3 × 3 = 9. Now the quotient is 3, and the remainder is 9 - 9 = 0.

Step 3: Bring down 41, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.

Step 4: The new divisor will be the sum of the old divisor and the quotient. Now we have 6n as the new divisor; we need to find the value of n.

Step 5: Find 6n × n ≤ 41. Let us consider n as 5: 6 × 5 = 30, and 30 × 5 = 150.

Step 6: Subtract 150 from 41, which is not possible, so consider n as 4: 6 × 4 = 24, and 24 × 4 = 96.

Step 7: Subtract 96 from 410 (by bringing down another pair of zeroes due to decimal point addition) to get 314.

Step 8: Continue the process to get the decimal expansion of the square root of 941.

So the square root of √941 ≈ 30.672.

The approximation method is another method for finding square roots; it is an easy method to approximate the square root of a given number. Now let us learn how to find the square root of 941 using the approximation method.

Step 1: Find the closest perfect squares to √941. The smallest perfect square less than 941 is 900, and the largest perfect square more than 941 is 961. √941 falls somewhere between 30 and 31.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (941 - 900) / (961 - 900) = 41/61 ≈ 0.672.

Using the approximation, add the initial integer value to the decimal: 30 + 0.672 = 30.672.

So, the square root of 941 is approximately 30.672.

• Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, which is √16 = 4.

• Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.

• Prime number: A prime number has exactly two distinct factors: 1 and itself. Example: 941 is a prime number.

• Long division method: A method used to find square roots of non-perfect squares through a series of division steps.

• Approximation method: A method used to estimate the square root of a number by finding nearby perfect squares and interpolating between them.