Q&A for How to Calculate Cube Root by Hand

The cube root of 27 is 3, and 3 raised to the sixth power is 729.

The fourth root is the square root of the square root.

This question might be simplest to solve using the repeated estimation method described in the article. You should know that the cube root must be nearly 3, since 3 cubed is 27, and 24 is very close to 27. So you could first estimate that the cube root is 2.8. You'll find that 2.8 cubed is 21.952, and 2.9 cubed is 24.389. Thus, the cube root of 24 is a bit more than 2.8 but less than 2.9. The target of 24 is very near to 24.389, so choose a number closer to 2.9 than 2.8. Estimate 2.88. You'll find that 2.88 cubed is 23.888, but 2.89 cubed is 24.138. So the solution is between 2.88 and 2.89, almost exactly in the middle. So the next estimate would be 2.885. Then continue as long as you like for precision.

No. The algorithm works just fine. You should check your sources and recheck your work. This could be a question of precision. When you begin by saying "the cube root of 9 is 2.080," what is your source for that? 2.080 cubed = 8.9989. When written without decimals, this means 2.080 cubed is 9. 2.081 cubed = 9.0119. When written without decimals, this means 2.081 cubed is 9. 2.082 cubed = 9.0249. When written without decimals, this means 2.082 cubed is 9. In fact, you can go as high as 2.11, cubed, and still say that the result is 9.

The process described in this article works for solving the cube roots of numbers less than 1 as well as numbers greater than 1. You will set up the problem in just the same way. Remember to write the numbers in groups of 3 digits, beginning at the decimal point. In this case, you will write 0.04 as 0.040 000 000. Each group of three digits will result in one digit of your solution. The work is too lengthy to write out here. The solution, to three decimal places, is 0.341.

Squaring is multiplying a number by itself. Cubing is multiplying the square by the base number again.

According to Pascal's triangle coefficients, the first line is 1 for 0th power,2nd line is11,3rd line is 121 for squared and the fourth line is 1331 for the cube of 11.In reverse,the cube root of 1331 is 11.

This answer only works simply and cleanly because you have selected .001. This is not so hard, but again only because it's this number. 3√.001=x is equal to x^3 = .001, and since we are only talking about .001, consider that .001 is actually 1 thousandth so consider what whole x^3 would give you 1,000. This means your answer would be 1000's cubed root. 10 x 10 x 10 = 1000, but we have the decimal, meaning 10 but 1 tenth would be the cubed root of 1 thousandth, or .1 x .1 x .1= .001 and the inverse 3√.001=.1.

Start with knowing that 2 cubed is 8. From there, you already know that the cube root of 7.97 will be just under 2, since 7.97 is just under 2 cubed. With that knowledge, you can guess 1.99. This gives 7.88, which isn't close enough. Try 1.999. You get 7.988, which is a little too high. Try 1.995. You get 7.94, which is too low. Try 1.998. You get 7.976, which is very close. If you want to be more specific, you can try numbers between 1.997 and 1.998, like 1.9976, and you can continue getting closer and closer. The basic idea is to try a number, then see if that number is too high or too low. If it's too low, increase it. If it's too high, lower it.

There are several guides on wikiHow that can help you find square roots, like How to Calculate a Square Root by Hand and How to Find a Square Root Without a Calculator .

Logically, it's ½, because ½ x ½ x ½ = 1/8. Another way to approach it is: the cube root of 1/8 is the same as the cube root of 1, which is 1, divided by the cube root of 8, which is 2. Thus, ½.

Starting with 9, the first digit has to be 2 because 2³ = 8 and 3³ = 27. Subtract 8 from 9 to get 1, then bring down three zeroes to get 1 000. 300*2² = 1 200, which is bigger than 1 000 so the next digit is 0. Bring down another three zeroes to get 1 000 000. 300*20² = 120 000; 8*120 000 is 960 000 which is close to 1 000 000 so try 8 as next digit. 300*20² + 30*20*8 + 8² = 124 864, multiply by 8 to get 998 912. Subtract to get 1 088, bring down three zeroes to get 1 088 000. 300*208² = 12 979 200 which is much bigger than 1 088 000, so next digit is 0. The cube root of 9 to three decimal places is 2.080.

By the repeated estimation method shown in Part 2 above (using a simple calculator), you can estimate the cube root of 3 to be 1.4423. (It takes between five and ten minutes to do that.)

First convert it to a decimal number, and then use one of the methods shown above.

Do the same steps as described in the article. Just write the decimal (e.g. 6.28) on the first line and fill with trailing zeroes, so instead of 10.000 000, you write 6.280 000. Same if you do just decimals: if you want to find the cube root of 0.707, you write down 0.707 000. Multiple sets of 000s are okay, for bigger accuracy.

Multiply your answer by itself twice. In other words, cube your answer. If your answer is correct, you will get the original number.