36√39/9√13
To simplify this expression, we can first simplify the radicals in the numerator and denominator separately:
√39 can be simplified to √(13 * 3), which is √13 * √3.
√13 cannot be simplified further.
Similarly, √13 can be simplified to √(13 * 1), which is √13.
Now, the expression becomes:
(36 * √13) / (9 * √13)
Next, we can simplify the fraction:
36 / 9 is equal to 4.
The final simplified expression is 4 * √13.
So, 36√39/9√13 simplifies to 4√13.
To simplify the expression 36√39/9√13, follow these steps:
Step 1: Simplify the numerator
36√39 simplifies to 6√(4⋅9⋅39).
= 6√(4⋅(9⋅39))
= 6√(4⋅(351))
= 6√(1404)
Step 2: Simplify the denominator
9√13 simplifies to 3√(3⋅3⋅13).
= 3√(3⋅(3⋅13))
= 3√(3⋅(39))
= 3√(117)
Step 3: Combine the simplified numerator and denominator
= (6√(1404))/(3√(117))
Step 4: Simplify the radicals if possible
The square root of 117 is not a perfect square, so it cannot be simplified further.
Step 5: Divide the coefficients and simplify
= 6/3 * (√(1404)/√(117))
= 2 * (√(1404)/√(117))
= 2 * (√(4⋅9⋅39)/(3⋅√(13)))
= 2 * (√(4)⋅√(9)⋅√(39)/(3⋅√(13)))
= 2 * (2⋅3⋅√(39)/(3⋅√(13)))
= 2 * (2⋅√(39)/√(13))
= 2 * (2⋅(√(39)⋅√(13)/(√(13)⋅√(13)))
= 2 * (2⋅(√(39)⋅√(13)/(√(13)^2))
= 2 * (2⋅(√(39)⋅√(13)/13))
= 2 * (2⋅(√(507)/13))
Step 6: Simplify the expression further if needed
The expression 2⋅(√(507)/13) cannot be simplified further.
So, the simplified expression is 2⋅(√(507)/13).
To simplify the expression (36√39)/(9√13), you can follow these steps:
Step 1: Simplify the numerator and denominator separately.
36√39 can be simplified by splitting the number 39 into its prime factors: 39 = 3 × 13. Now, we can simplify the square root of 39 by taking out the square root of its perfect square factors, which in this case is 13. Therefore, 36√39 = 6√13.
Similarly, for the denominator 9√13, we can see that 9 is a perfect square. Thus, we can simplify it as 9 = 3^2. Now, the square root of 9 is simply 3. Hence, 9√13 = 3√13.
Now, the expression becomes (6√13)/(3√13).
Step 2: Cancel out common factors in the numerator and denominator.
Since both the numerator and denominator have √13, we can cancel them out, resulting in 6/3.
Step 3: Simplify the fraction.
Dividing 6 by 3 gives us the simplified fraction 2.
Therefore, the expression (36√39)/(9√13) simplifies to 2.