Divide 36√39 / 9√13 . Provide an exact answer.
To divide the given expression, we need to rationalize the denominator.
First, we multiply the numerator and denominator by the conjugate of the denominator:
= (36√39 / 9√13) * (√13 / √13)
= (36 * √39 * √13) / (9 * √13 * √13)
= (36 * √507) / (9 * 13)
= (36 * √507) / 117
= (4 * 9 * √507) / 117
= (4/117) * (9√507)
Therefore, the exact answer is (4/117) * (9√507).
To divide the given expression 36√39 / 9√13, we can simplify it step by step.
Step 1: Simplify the numerator and denominator individually.
The square root of 39 can be simplified as the product of the square root of its factors:
√39 = √(3 × 13) = √3 × √13.
Similarly, the square root of 13 can be simplified as √13.
Therefore, we can rewrite the expression as: (36 × √3 × √13) / (9 × √13).
Step 2: Simplify the expression further by canceling out common factors.
We can cancel out the √13 term in the numerator and denominator, leaving us with:
36 × √3 / 9
Step 3: Simplify the remaining expression.
Dividing 36 by 9 gives us the result: 4.
So, the final exact answer is: 4√3.
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To divide 36√39 by 9√13, we can simplify it step by step.
Step 1: Simplify the numerator and denominator individually.
The square root of 39 cannot be simplified any further.
The square root of 13 cannot be simplified any further.
Therefore, the expression remains: (36√39) / (9√13).
Step 2: Combine like terms in the numerator and denominator.
The expression simplifies to: (36 / 9) * (√39 / √13).
Step 3: Simplify the expression further.
Dividing 36 by 9 gives us the result: 4.
The square roots of 39 and 13 cannot be simplified any further.
Therefore, the final exact answer is: 4 * (√39 / √13), or simply 4√(39/13).
To divide the expression 36√39 / 9√13, we can simplify it by rationalizing the denominator.
First, let's multiply the numerator and denominator by the conjugate of the denominator to rationalize it.
The conjugate of 9√13 is (-9√13), so we multiply the expression by (-9√13) / (-9√13):
(36√39 / 9√13) * (-9√13 / -9√13)
Now, we can simplify by multiplying the numerators and multiplying the denominators:
(36 * -9) * (√39 * √13) / (9 * -9 * √13 * √13)
Simplifying further:
-324√507 / -117
The negatives in the numerator and denominator cancel each other out, so we can remove them:
324√507 / 117
So, the exact answer to the expression 36√39 / 9√13 is 324√507 / 117.