solve: (36√39) / (9√13)
To simplify the expression, we can start by simplifying the square roots and dividing the numbers:
(36√39) / (9√13) = (6√(3*13)) / (3√13)
Since both square roots have the same number inside (13), we can cancel them out:
= 6√3
Therefore, the simplified expression is 6√3.
To solve the expression (36√39) / (9√13), we can start by simplifying the terms under the square roots:
√39 can be simplified as √(3 * 13). Taking out the perfect square, we have:
√39 = √(3 * 13) = √3 * √13
Similarly, √13 can't be simplified further.
Now, let's substitute these simplified values back into the original expression:
(36√39) / (9√13) = (36 * √3 * √13) / (9 * √13)
Next, let's simplify the coefficients separately:
36 / 9 = 4
√3 / 1 = √3
Substituting these values back into the expression, we have:
(4 * √3 * √13) / (1 * √13)
Now, the √13 terms cancel out:
(4 * √3 * √13)/(1 * √13) = 4√3
Therefore, the simplified expression is 4√3.
To solve the expression (36√39) / (9√13), we can simplify it by dividing the numbers separately and then dividing the square roots separately.
Step 1: Divide the numbers:
36 divided by 9 is equal to 4.
Step 2: Divide the square roots:
√39 divided by √13 can be simplified by rationalizing the denominator. To do this, we multiply both the numerator and denominator by √13.
(√39 / √13) * (√13 / √13) becomes (√(39 * 13) / √(13 * 13)).
Simplifying this further, we have:
√507 / √169
Step 3: Simplify the square roots:
√507 can be simplified by breaking down 507 into its prime factors.
507 = 13 * 39
Now we can rewrite the square root as:
√(13 * 39)
Taking out the perfect square factors:
√13 * √39
Finally, we can rewrite the entire expression as:
4 * (√13 * √39) / √169
Step 4: Simplify the expression:
√169 is equal to 13.
So the expression becomes:
4 * (√13 * √39) / 13
Now, we can multiply the numbers and simplify the square roots:
4 * (√(13 * 39)) / 13 = 4 * (√(507)) / 13 = (4√507) / 13
Therefore, the simplified form of (36√39) / (9√13) is (4√507) / 13.