Find the cube root of 81
The cube root of 81 is 4.326749.
To find the cube root of 81, you can take the number 81 and determine the number that, when multiplied by itself twice, gives the result of 81.
1. Start by guessing a number to find the approximate cube root. Let's start with the number 4.
2. Cube 4 by multiplying it by itself twice: 4 x 4 x 4 = 64.
3. Since 64 is less than 81, we need to try a larger number.
4. Let's try the number 5. Cube 5 by multiplying it by itself twice: 5 x 5 x 5 = 125.
5. Since 125 is greater than 81, we need to try a smaller number.
6. Let's now try the number 4.5 as an approximation.
7. Cube 4.5 by multiplying it by itself twice: 4.5 x 4.5 x 4.5 = 91.125.
8. Since 91.125 is larger than 81, we need to try a smaller number.
9. Let's now try the number 4.2 as an approximation.
10. Cube 4.2 by multiplying it by itself twice: 4.2 x 4.2 x 4.2 = 74.088.
11. Since 74.088 is less than 81, we need to try a larger number.
12. Let's now try the number 4.3 as an approximation.
13. Cube 4.3 by multiplying it by itself twice: 4.3 x 4.3 x 4.3 = 82.347.
14. Since 82.347 is larger than 81, we need to try a smaller number.
15. Let's now try the number 4.25 as an approximation.
16. Cube 4.25 by multiplying it by itself twice: 4.25 x 4.25 x 4.25 = 81.266.
17. Since 81.266 is slightly larger than 81, we can assume that the cube root of 81 is slightly smaller than 4.25.
18. By trying out smaller numbers, we find that 4.25 is already a good approximation.
19. Therefore, the cube root of 81 is approximately 4.25.
To find the cube root of a number, you can use a calculator or calculate it manually using arithmetic operations. Here's the step-by-step process to find the cube root of 81:
1. If you have a scientific calculator, you can use the cube root function. Simply input 81, then press the cube root button (usually denoted as "^3√" or "yx" on the calculator). The result will be displayed.
2. If you don't have a calculator, you can calculate the cube root manually by repeated approximation. Start by guessing the cube root of 81. Since 4^3 = 64 and 5^3 = 125, you can make an educated guess that the cube root of 81 is between 4 and 5.
3. To narrow down the approximation, try a number between 4 and 5, like 4.5. Calculate 4.5^3 using multiplication: 4.5 * 4.5 * 4.5 = 91.125. Since this is greater than 81, you know the cube root must be less than 4.5.
4. Now, try a smaller number between 4 and 4.5. Let's use 4.4. Calculate 4.4^3: 4.4 * 4.4 * 4.4 = 85.184. Since this is still greater than 81, you can refine your approximation to be between 4 and 4.4.
5. Repeat this process with smaller increments until you find a number whose cube is very close to 81. Eventually, you will find that 4.3^3 = 79.507, and 4.4^3 = 84.224. Since 81 is closer to 79.507, you can say that the cube root of 81 is approximately 4.3.
Note: This method is an approximation and may not give you the exact value of the cube root. To get the precise decimal value, you can use a calculator or a more advanced mathematical technique.