Divide 36√39 / 9√13. Provide an exact answer.
To divide the two given terms, we simplify the expression as follows:
36√39 / 9√13
First, we divide the numbers outside the square roots: 36 / 9 = 4.
Next, we divide the numbers inside the square roots: √39 / √13 = √(39/13) = √3.
Now, we have 4√3 as the simplified expression.
To divide the expression 36√39 / 9√13, we can simplify it as follows:
Step 1: Divide the numerical coefficients:
36 / 9 = 4
Step 2: Divide the square roots:
√39 / √13
To simplify the division of square roots, we can rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator. The conjugate of √13 is -√13.
(√39 / √13) * ( -√13 / -√13)
This results in:
-√507 / -13
Step 3: Simplify the negative signs:
-√507 / -13 = √507 / 13
Therefore, the exact answer to the expression 36√39 / 9√13 is √507 / 13.
To divide the expression (36√39) / (9√13) and provide an exact answer, we can follow these steps:
Step 1: Simplify the expressions under the square roots.
√39 = √(3 * 13) = √3 * √13
√13 = √13
Step 2: Simplify the expression by canceling out common factors.
(36 * √3 * √13) / (9 * √13)
We can cancel out the common factor of 3 between the numerator and the denominator:
(12 * √3) / (3 * √13)
Step 3: Simplify further by canceling out the remaining common factors.
12 / 3 = 4
The final expression is:
4√3 / √13
This is the exact answer to the division.