



 
Hi Jacqui, This is a useful technique to learn because it allows you to estimate cube roots or other roots. The number you have is an 8 followed by three zeros and I know that 10 10 10 = 10^{3} = 1000 so I think that the cube root of 8000 is probably a two digit number with the units digit 0, that is a number d0 where d is a one digit number. So what is d to give me a cube of 8000? I know that 2 2 2 = 8 so 20^{3} = 8000. But 8000 is quite special, it is the cube if an integer whereas most integers are not cubes of integers. For example what is the cube root of 9413? I don't know but I can find an estimate quite easily. As I observed with 8000 the cube root of 9413 is approximately a two digit number. (9413 = 9000 + 413 and the 3 zeros tell me to try d0 again.) 20^{3} = 8000 and 30^{3} = 27000 so the cube root of 9413 is between 20 and 30 and probably much close to 20 than 30. So far I have only used mental arithmetic. Next I tried 22^{3} and calculated it with paper and pencil and found that 22^{3} = 10648. Hence the cube root of 9413 is largest than 20 and smaller than 22. If you need a better estimate try 21^{3} and see if the cube root of 9413 is larger than or smaller than 21. Penny  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 