Find the cubic root of 135.
^3V5
3^3V5
5^3^27
3V5
The cubic root of 135 is approximately 5.032.
To find the cubic root of 135, you can use the notation "∛135" or "135^(1/3)".
Using a calculator, the cubic root of 135 is approximately 5.261. So, ∛135 ≈ 5.261.
Alternatively, you can simplify the calculation using prime factorization:
1. Start by finding the prime factors of 135: 135 = 3 × 3 × 3 × 5.
2. Group the prime factors in sets of three: (3 × 3) × (3 × 5).
3. Take out one factor from each set (the cube root): 3 × 3 × 5 = 45.
4. The result is 45. So, ∛135 = 45.
To find the cubic root of a number, you can either use a calculator that has a cubic root function, or you can manually solve it using basic arithmetic operations.
1. Using a calculator:
Simply input the number 135 and apply the cubic root function (^3√) to get the result. The exact calculation may vary depending on the calculator you are using.
2. Manually solving:
Start by making an educated guess for the approximate solution. In this case, we can try guessing that the cubic root of 135 is around 5. The reason behind this guess is that 5^3 = 125, which is close to 135.
- Test the guess:
Cube the guessed number. In this example, compute 5^3 = 5 * 5 * 5 = 125. Since the result is less than 135, we need to increase our guess.
- Refine the guess:
Increment the guess by a small amount and repeat the previous step until we get an approximate solution. In this case, let's increment the guess by 0.1: 5 + 0.1 = 5.1.
- Test the refined guess:
Cube the refined guess. Compute 5.1^3 = 5.1 * 5.1 * 5.1 ≈ 132.65.
Since the result is still less than 135, we need to continue refining the guess.
- Iterate and refine:
Repeat the previous step by incrementing the guess by small amounts and testing each refined guess until you find a result that is close to 135.
Continuing this process, we find that the cubic root of 135 is approximately 5.16.
Therefore, the cubic root of 135 is roughly 5.16.