Find the cube root of 81: ∛81
∛81
-9
9
27
4.3267487109222245
To find the cube root of 81, you can use a calculator or manually trial and error.
By manually trial and error, you can start by guessing a number and then checking if the cube of that number equals 81.
Let's start with -9:
(-9)³ = -9 x -9 x -9 = -729
Since -729 is not equal to 81, -9 is not the cube root of 81.
Now let's try 9:
(9)³ = 9 x 9 x 9 = 729
Since 729 is not equal to 81, 9 is not the cube root of 81.
Finally, let's try 27:
(27)³ = 27 x 27 x 27 = 19683
Since 19683 is not equal to 81, 27 is not the cube root of 81.
After trying the possible options, we can conclude that none of the numbers -9, 9, and 27 are the cube root of 81.
Therefore, the cube root of 81, expressed mathematically, is ∛81.
To find the cube root of a number, you can use a calculator or perform the calculation manually. Let's go through the steps to find the cube root of 81.
Method 1: Using a calculator:
1. Open up the calculator on your computer or smartphone.
2. Look for the symbol "^" or "y√x" on the calculator.
3. Enter the number 81.
4. Press the "^" or "y√x" button.
5. Enter the exponent of 1/3 or 0.3333333.
6. Press the "=" or "Enter" button.
7. The calculator should display the result, which is 4.3267487109222245.
Method 2: Manual calculation:
Now, let's calculate the cube root of 81 manually:
1. Start by guessing a number as the cube root of 81.
2. Let's begin with the number 3.
3. Cube 3: 3 * 3 * 3 = 27.
4. Since 27 is less than 81, we can guess a larger number.
5. Let's try 4. Cube 4: 4 * 4 * 4 = 64.
6. Since 64 is still less than 81, we can guess a larger number.
7. Let's try 5. Cube 5: 5 * 5 * 5 = 125.
8. Since 125 is greater than 81, we can try smaller numbers.
9. Let's go back to 4. Cube 4: 4 * 4 * 4 = 64.
10. Since 64 is less than 81, we know that the cube root must be between 4 and 5.
11. We can make an educated guess and try 4.5.
12. Cube 4.5: 4.5 * 4.5 * 4.5 = 91.125.
13. Since 91.125 is also greater than 81, we know the cube root must be slightly less than 4.5.
14. We can continue to refine our guess, considering smaller increments like 4.4, 4.3, etc.
15. Continuing this process, we eventually find that 4.326 is a good approximation for the cube root of 81.
So, the cube root of 81 is approximately 4.326.