Square Root of 930

The square root is the inverse of squaring a number. 930 is not a perfect square. The square root of 930 is expressed in both radical and exponential form. In the radical form, it is expressed as √930, whereas in exponential form it is (930)^(1/2). √930 ≈ 30.495, 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 used for non-perfect square numbers, where 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 930 is broken down into its prime factors.

Step 1: Finding the prime factors of 930 Breaking it down, we get 2 x 3 x 5 x 31: 2^1 x 3^1 x 5^1 x 31^1

Step 2: Now we have found the prime factors of 930. Since 930 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating √930 using prime factorization is not feasible.

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 930, we need to group it as 30 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 x 3 = 9. Now the quotient is 3, and after subtracting 9 - 9, the remainder is 0.

Step 3: Bring down 30, 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 6n. We need to find the value of n such that 6n x n ≤ 30. Let us consider n as 5, now 65 x 5 = 325, which is too large. Instead, try n as 4: 64 x 4 = 256.

Step 5: Subtract 30 from 25, and the difference is 5. The quotient is 3.4.

Step 6: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal allows us to add two zeroes to the dividend. Now the new dividend is 500.

Step 7: Find the new divisor: 69 because 694 x 4 = 276.

Step 8: Subtract 276 from 500, resulting in 224. Step 9: Now the quotient is 30.49.

Step 10: Continue these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue until the remainder is zero.

So the square root of √930 is approximately 30.495.

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 930 using the approximation method.

Step 1: We need to find the closest perfect squares to √930.

The smallest perfect square less than 930 is 900, and the largest perfect square greater than 930 is 961.

√930 falls somewhere between 30 and 31.

Step 2: Now we need to apply the formula:

(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).

Using the formula (930 - 900) / (961 - 900) = 30/61 ≈ 0.49.

Adding the initial whole number to the decimal gives us: 30 + 0.49 ≈ 30.49.

Therefore, the square root of 930 is approximately 30.49.

• Square root: A square root is the inverse of squaring a number. For example, 4^2 = 16, and the inverse is the square root: √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.
   
• Approximation: An approximation is a value or quantity that is nearly but not exactly correct; it is used when a precise answer is not feasible.
   
• Long division method: A step-by-step method used to divide numbers to find the square root of non-perfect squares.
   
• Decimal: A number that includes a whole number and a fractional part, separated by a decimal point, such as 7.86, 8.65, and 9.42.