Square Root of 439

The square root is the inverse of the square of a number. 439 is not a perfect square. The square root of 439 is expressed in both radical and exponential form. In the radical form, it is expressed as √439, whereas in exponential form it is (439)^(1/2). √439 ≈ 20.9523, 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 long-division and approximation methods 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 439 is broken down into its prime factors.

Step 1: Finding the prime factors of 439 439 is a prime number itself, and therefore it cannot be broken down into other prime factors besides 1 and 439. Since 439 is not a perfect square, calculating 439 using prime factorization for its square root 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 439, we need to group it as 39 and 4.

Step 2: Now we need to find n whose square is less than or equal to 4. We can say n as ‘2’ because 2 x 2 is 4. Now the quotient is 2 after subtracting 4-4 the remainder is 0.

Step 3: Now let us bring down 39 which is the new dividend. Add the old divisor with the same number 2 + 2 we get 4 which will be our new divisor.

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

Step 5: The next step is finding 4n x n ≤ 39. Let us consider n as 9, now 49 x 9 = 441, which is greater than 39, so try n as 8.

Step 6: Subtract 39 from 48 (which is 4 x 8), the difference is -9, and the quotient is 20.8

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 900.

Step 8: Now we need to find the new divisor that is 209 because 209 x 4 = 836.

Step 9: Subtracting 836 from 900 we get the result 64.

Step 10: Now the quotient is 20.9

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values continue till the remainder is zero.

So the square root of √439 is approximately 20.95.

Approximation method is another method for finding the 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 439 using the approximation method.

Step 1: Now we have to find the closest perfect square of √439. The smallest perfect square less than 439 is 400 and the largest perfect square greater than 439 is 441. √439 falls somewhere between 20 and 21.

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (439 - 400) ÷ (441 - 400) = 39 / 41 ≈ 0.9512. Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 20 + 0.9512 = 20.9512.

So the square root of 439 is approximately 20.9512.

• Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root that 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 is a number greater than 1 that has no positive divisors other than 1 and itself.

• Decimal: A decimal is a number that has a whole number and a fraction in a single number. For example: 7.86, 8.65, and 9.42 are decimals.

• Perfect square: A perfect square is a number that is the square of an integer. For example: 1, 4, 9, 16, and 25 are perfect squares.