Find the cubic root of 135.
3\sqrt(5)
5 * root(27, 3)
3 * root(5, 3)
\root(3)(5)
The cubic root of 135 is 3 * root(5, 3).
To find the cubic root of 135, we can use a calculator or compute it manually. Here's a step-by-step method to find the cubic root of 135 manually:
Step 1: Start by dividing 135 by small perfect cubes until there is no perfect cube left as a factor.
135 ÷ 2 = 67.5
135 ÷ 3 = 45
135 ÷ 4 = 33.75
...
Step 2: Continue dividing until there is no perfect cube left as a factor. In this case, there are no more small perfect cubes left, so we can proceed to the next step.
Step 3: Use estimation to find the largest perfect cube that is less than or equal to the remaining number. In this case, 4^3 is the largest perfect cube that is less than 135.
4^3 = 64
Step 4: Divide the remaining number by the value obtained in the previous step.
135 ÷ 64 ≈ 2.109375
Step 5: Estimate the cubic root of the remaining decimal value obtained in the previous step. In this case, you can estimate it as approximately 1.25.
Step 6: Multiply the estimated value from the previous step by the value obtained in step 3.
1.25 x 4 = 5
Therefore, the cubic root of 135 is approximately 5.
To find the cubic root of a number, you need to find the number that, when multiplied by itself three times, equals the given number.
In this case, we want to find the cubic root of 135.
One way to calculate the cubic root of 135 is to use a calculator. Most scientific calculators have a cubic root function. On such a calculator, you would enter 135 and then use the cubic root function to get the answer, which is approximately 5.75.
Another way to find the cubic root is using the radical notation. To write the cubic root of 135 using radical notation, you would write it as ∛135.
However, if you are looking for a simplified form of the cubic root, you can break down the number into its prime factors.
The prime factorization of 135 is: 3 × 3 × 3 × 5.
Now, we group the prime factors in sets of three because we are looking for the cubic root. We have one group of three 3s and one 5.
So, the simplified form of the cubic root of 135 can be written as:
∛(3 × 3 × 3 × 5)
Taking one 3 and one 5 out of the cube root, it becomes:
3∛5
Therefore, the cubic root of 135 is 3∛5.