The concept of a root from the fourth degree can be considered on the example of the look equation: x*x*x*x=y. A fourth root from number y is x. From this equation it is visible that the number from which the root is taken cannot be negative. The root from zero gives zero. To find x it is possible in several ways.
It is required to you
- Calculator, either computer, or sheet of paper and handle.
Instruction
1. It is possible to calculate a fourth root if twice to take a square root from number. On the majority of calculators there is a function of extraction of a square root. Such function is in utility programs of Windows. On the Internet there are also online programs.
2. It is possible to calculate a fourth root, having built number y in degree ¼ or 0.25. It is possible to make it in the Microsoft Excel program. Enter in a line of functions: =y^ (1/4) or =y^0.25. Having pressed "Enter", you receive the answer in the allocated cell.
3. If near at hand there is no equipment, it is possible to find approximate value of a root an iteration method, i.e. repetitions. Take number, increase by yourself four times, compare result to number y. Then take other number, it is more or less previous, depending on result. So repeat several times, yet do not receive result of sufficient accuracy.
4. Also there is an interesting algorithm of calculation of square roots. Having used it twice, you receive a fourth root. Let's consider it on the example of number 7072781.
5. Beginning on the right, separate two figures: 70.72.81. Pick up the greatest number which square will be less than 70 - the first part of number – 8. It is the first figure of your result.
6. Square this figure and subtract from 70: 70-64=6. Attribute it to the second part of number at the left – 672. Double the first figure of result: 8*2=16. Then find the greatest number, having attributed which to 16 and having increased by it the received figure, you receive the greatest result which is not exceeding 672: 164*4=656
7. Further act so: 672-656=16 you Attribute 16 to the third part at the left – 1681. You double 84 – two already known figures of result: 84*2=168. You find number, having added which on the right and having increased by it, you receive this time exactly 1681: 1681*1=1681. Figure 1 is the third sign of the answer. The square root from 7072781 is equal to 841.
8. If you did not receive equality, it is necessary to repeat operation to find answer figures after a comma. Two zero will be two figures of the following part. Calculations are made before achievement of necessary accuracy of the answer. If in your number there were still parts, also repeat operation. Then you apply all algorithm from the very beginning and you take a square root from number 841. The received answer - 29.