Divide 36√39 / 9√13
To divide these two expressions, we can simplify them individually and then divide the results.
First, let's simplify 36√39:
√39 = √(3*13) = √(3) * √(13) = √3√13
36√39 = 36 * √3√13 = 6√3 * 6√13 = 216√39
Next, let's simplify 9√13:
9√13 = 3√13 * 3 = 9√13
Now we can divide the simplified expressions:
(216√39) / (9√13) = (216 / 9) * (√39 / √13) = 24 * (√(39/13)) = 24 * √3
Therefore, 36√39 / 9√13 simplifies to 24√3.
To divide 36√39 by 9√13, we will follow these steps:
Step 1: Simplify both radicals:
36√39 can be simplified as 6√169
9√13 can be simplified as 3√13
Step 2: Divide the numbers outside the radicals:
6 divided by 3 is 2.
Step 3: Divide the numbers inside the radicals:
√169 divided by √13 is √(169/13)
Step 4: Simplify the square root:
√(169/13) = √(13/1) = √13
Step 5: Combine the result from steps 2 and 4:
2√13 is the final result of the division.
Therefore, 36√39 / 9√13 = 2√13.
To divide these expressions, you need to rationalize the denominator. Rationalizing the denominator means multiplying both the numerator and the denominator by a suitable expression to eliminate any square roots in the denominator.
Let's proceed with the division step-by-step:
Step 1: Start with the given expression: 36√39 / 9√13.
Step 2: Rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator. In this case, the conjugate of 9√13 is 9√13.
(36√39 / 9√13) * (9√13 / 9√13)
Step 3: Simplify both the numerator and the denominator:
(36 * 9 * √39 * √13) / (9 * 9 * √13 * √13)
Step 4: Cancel out like terms:
(36 * √3 * √13) / (3 * 13)
Step 5: Simplify the expression further:
(4 * √3 * √13) / (1 * 13)
Step 6: Multiply and simplify:
(4 * 13 * √3) / 13
Step 7: Cancel out like terms:
(4 * √3 * 1)
Step 8: Finally, simplify the expression:
4√3
Therefore, 36√39 / 9√13 simplifies to 4√3.