how to calculate manually( 3.57)power 1/3
(1/10) (3570)^1/3
= (1/10)(15.3) = 1.53 approx
This kind of thing is what log tables were used for.
Now we have calculators.
To calculate (3.57)^(1/3) manually, you can follow these steps:
Step 1: Estimate the cube root value.
Start by finding the closest whole number to the cube root of the given number. In this case, the number is 3.57. The closest whole number to the cube root of 3.57 is 1.
Step 2: Square the estimated value.
Take the estimation from step 1 (1) and square it. In this case, 1 squared is 1.
Step 3: Multiply the squared value by the estimated value.
Take the result from step 2 (1) and multiply it by the estimation from step 1 (1). In this case, 1 multiplied by 1 is 1.
Step 4: Compare the result to the given value.
Compare the result from step 3 (1) to the original value given, which is 3.57.
Step 5: Adjust the estimation.
If the result from step 3 is less than the given value, increase the estimation from step 1 by 1. In this case, since 1 is less than 3.57, you need to increase the estimation.
Step 6: Repeat steps 2-5.
Repeat steps 2-5 with the adjusted estimation until you find a result that is close to the given value. Each time, increase the estimation by 1.
By following this process, you can continue adjusting your estimation until you find a result that is close to the given value. Remember, this method may involve some trial and error until you reach the desired level of accuracy.