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.  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. You will use these in the computations. These cubes are as follows:  13=1∗1∗1=1{\displaystyle 1^{3}=1*1*1=1} 23=2∗2∗2=8{\displaystyle 2^{3}=2*2*2=8} 33=3∗3∗3=27{\displaystyle 3^{3}=3*3*3=27} 43=4∗4∗4=64{\displaystyle 4^{3}=4*4*4=64} 53=5∗5∗5=125{\displaystyle 5^{3}=5*5*5=125} 63=6∗6∗6=216{\displaystyle 6^{3}=6*6*6=216} 73=7∗7∗7=343{\displaystyle 7^{3}=7*7*7=343} 83=8∗8∗8=512{\displaystyle 8^{3}=8*8*8=512} 93=9∗9∗9=729{\displaystyle 9^{3}=9*9*9=729} 103=10∗10∗10=1000{\displaystyle 10^{3}=10*10*10=1000} Select a number that, when cubed, gives the largest possible result less than the first set of three numbers.  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 23{\displaystyle 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 23{\displaystyle 2^{3}} is only 8, not very close to 10, you should continue. 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. 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. 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. Find the next digit of your solution by selecting what you can multiply by the divisor, 1200-something, to then subtract from the remainder of 2000. This can only be 1, since 2 times 1200 would be 2400, which is greater than 2000. Write the number 1 in the next space above the radical sign. The divisor for this step of the solution is made up of three parts. The first part is the 1200 that you already have. You need to add two more terms to that to complete the divisor.  Now calculate 3 times 10 times each of the two digits that are in your solution above the radical sign. For this sample problem, that means 3*10*2*1, which is 60. Add this to the 1200 that you already have to make 1260. Finally, add the square of the last digit. For this example, that is a 1, and 1^2 is still 1. The total divisor is, therefore 1200+60+1, or 1261. Write this to the left of the vertical line. Complete this round of the solution by multiplying the last digit of your solution - in this case, the number 1 - times the divisor you just calculated, 1261. 1*1261 =1261. Write this under the 2000, and subtract, to give 739. After you complete the subtraction portion of each step, you need to consider whether your answer is precise enough. For the cube root of 10, after the first subtraction, your cube root was just 2, which is not very precise. Now, after a second round, the solution is 2.1.  You can check the precision of this result by cubing 2.1*2.1*2.1. The result is 9.261. If you believe your result is precise enough, you can quit. If you want a more precise answer, then you need to proceed with another round. In this case, for more practice and a more precise answer, repeat the steps for another round, as follows:  Drop down the next group of three digits. In this case, these are three 0s, which will follow the 739 remainder to give 739,000. Begin the divisor with 300 times the square of the number currently above the radical line. This is 300∗212{\displaystyle 300*21^{2}}, which is 132,300. Select the next digit of your solution so that you can multiply it by 132,300 and have less than the 739,000 of your remainder. A good choice would be 5, since 5*132,300=661,500. Write the digit 5 in the next space above the radical line. Find 3 times the prior number above the radical line, 21, times the last digit you just wrote, 5, times 10. This gives 3∗21∗5∗10=3,150{\displaystyle 3*21*5*10=3,150}. Finally, square the last digit. This is 52=25.{\displaystyle 5^{2}=25.}  Add the parts of your divisor to get 132,300+3,150+25=135,475. After you have calculated the divisor for this next round and you have expanded your solution by one more digit, proceed as follows:  Multiply the divisor by the last digit of your solution. 135475*5=677,375. Subtract. 739,000-677,375=61,625. Consider whether the solution of 2.15 is precise enough. Cube it to get 2.15∗2.15∗2.15=9.94{\displaystyle 2.15*2.15*2.15=9.94}. The result above the radical is the cube root, accurate at this point to three significant figures. In this example, the cube root of 10 is 2.15. Verify that by calculating 2.15^3=9.94, which approximates 10. If you need greater accuracy, simply continue the process as long as you desire.
एक प्रॉब्लम सेट करें: सिंगल डिजिट नंबर्स के क्यूब्स को जानें: अपने सोल्यूशन की पहली डिजिट को पाएँ: अगली डिजिट पाने के लिए सेटअप करें: नैक्सट डिवाइजर की शुरुआत पाएँ: अपने क्यूब रूट सोल्यूशन में नैक्सट नंबर पाएँ: डिवाइजर के बाकी के हिस्से को तय करें: मल्टीप्लाय और सब्ट्रेक्ट करें: तय करें, कि और ज्यादा एक्यूरेसी (शुद्धता) पाने के लिए और भी आगे बढ़ना है या नहीं: अगले राउंड के लिए डिवाइजर पाएँ: डिवाइजर को अपने सोल्यूशन नंबर से मल्टीप्लाय करें: अपने फ़ाइनल आन्सर को लिख लें: