Divide 933√2711√
. Provide an exact answer.
To divide 933 by √2711, multiply both the numerator and denominator by the conjugate of the denominator, which is √2711.
933/√2711 = (933/√2711) * (√2711/√2711)
= (933 * √2711) / (√2711 * √2711)
= (933 * √2711) / 2711
So the exact division of 933 by √2711 is (933 * √2711) / 2711.
To divide √933 by √2711, we can simplify each square root separately and then perform the division.
Simplifying √933:
To find the factors of 933, we can start by dividing it by the smallest prime number, which is 2. However, 933 is an odd number, so it is not divisible by 2. Let's try the next prime number, which is 3.
933 ÷ 3 = 311
Now, let's continue factoring 311. The next prime number after 3 is 5, but 311 is not divisible by 5 either. We can continue by checking all prime numbers up to the square root of 311, which is approximately 17.66.
By trying each prime number up to 17, we find that 311 is a prime number itself. Therefore, we cannot simplify √933 further.
Simplifying √2711:
Similarly, let's find the factors of 2711 by starting with the smallest prime number, which is 2.
2711 ÷ 2 = 1355.5
Since 1355.5 is not an integer, we continue factoring by trying the next prime number, which is 3.
2711 ÷ 3 = 903.67
Again, the result is not an integer. Continuing this process, we find that √2711 cannot be simplified further.
Now, let's perform the division:
√933 ÷ √2711 = (√933)/(√2711)
To simplify the division of two square roots, we will rationalize the denominator. This means we will multiply both the numerator and the denominator by the conjugate of the denominator.
The conjugate of √2711 is (-√2711), so we multiply both numerator and denominator by (-√2711):
[(√933)/(√2711)] * [(-√2711)/(-√2711)] = (-√933 * √2711) / (-√2711 * √2711)
= -√(933 * 2711) / -√(2711 * 2711)
= -√(2521263) / -2711
Therefore, the exact answer to √933 ÷ √2711 is -√(2521263) / -2711.
To divide √933 by √2711, we need to first rationalize the denominators.
Let's start by rationalizing √933:
√933 = √(9 * 104) = √(3^2 * 104) = 3√104.
Now, let's rationalize √2711:
√2711 = √(7 * 387) = √(7 * 3 * 129) = √(21 * 129) = √(3^2 * 7 * 129) = 3√(7 * 129) = 3√903.
Therefore, the division becomes:
(3√104) / (3√903).
Since both radicals have the same index and the same radicand (inside the square root), we can simplify this expression to:
(3/3) * (√104 / √903) = 1 * (√104 / √903) = √104 / √903.
So, the exact answer to √933 / √2711 is √104 / √903.