Evaluate:
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Answers
1
Set up the problem. Solving the cube root of a number is going to look like solving a long division problem, with a few special differences. The first step is to set up the problem in the proper format.[1]
Write down the number whose cube root you want to find. Write the digits in groups of three, using the decimal point as your starting place. For this example, you will find the cube root of 10. Write this as 10. 000 000. The extra 0s are to allow precision in the solution.
Draw a cube root radical sign over the number. This serves the same purpose as the long division bar line. The only difference is the shape of the symbol.
Place a decimal point above the bar line, directly above the decimal point in the original number.
2
Know the cubes of single digit numbers. You will use these in the computations. These cubes are as follows:
1^{3}=1*1*1=1}1^{3}=1*1*1=1
2^{3}=2*2*2=8}2^{3}=2*2*2=8
3^{3}=3*3*3=27}3^{3}=3*3*3=27
4^{3}=4*4*4=64}4^{3}=4*4*4=64
5^{3}=5*5*5=125}5^{3}=5*5*5=125
6^{3}=6*6*6=216}6^{3}=6*6*6=216
7^{3}=7*7*7=343}7^{3}=7*7*7=343
8^{3}=8*8*8=512}8^{3}=8*8*8=512
9^{3}=9*9*9=729}9^{3}=9*9*9=729
10^{3}=10*10*10=1000}10^{3}=10*10*10=1000
3
Find the first digit of your solution. Select a number that, when cubed, gives the largest possible result less than the first set of three numbers.[2]
In this example, the first set of three numbers is 10. Find the largest perfect cube that is less than 10. That number is 8, and its cube root is 2.
Write the number 2 above the radical bar line, over the number 10. Write the value of {\displaystyle 2^{3}}2^{3}, which is 8, underneath the number 10, draw a line and subtract, just as you would in long division. The result is a 2.
After the subtraction, you have the first digit of your solution. You need to decide if this one digit is a precise enough result. In most cases, it will not be. You can check by cubing the single digit and decide if that is close enough to the result you wanted. Here, because {\displaystyle 2^{3}}2^{3} is only 8, not very close to 10, you should continue.
4
Set up to find the next digit. Copy down the next group of three numbers into the remainder, and draw a small vertical line to the left of the resulting number. This will be the base number for finding the next digit in the solution of your cube root. In this example, this should be the number 2000, which is formed from the remainder 2 of the prior subtraction, with the group of three 0s that you pull down.[3]
To the left of the vertical line, you will be solving the next divisor, as the sum of three separate numbers. Draw the spaces for these numbers by making three blank underlines, with plus symbols between them.
5
Find the beginning of the next divisor. For the first part of the divisor, write down three hundred times the square of whatever is on top of the radical sign. In this case, the number on top is 2, 2^2 is 4, and 4*300=1200. So write 1200 in the first space. The divisor for this step of the solution will be 1200, plus something that you will find next.