How to take degree root 5

How to take degree root 5

The degree root n-y from number b is called such number a that a^n=b. Respectively, the root of the 5th degree from number b is the number a giving at construction in the fifth degree of b. For example, 2 – a root of the fifth degree from 32, since 2^5=32.


1. To take a root of the fifth degree, present subradical number or expression in the form of the fifth degree of other number or expression. It will also be required size. In certain cases such number is visible at once, in others it should be selected.

2. The sign for a root of the fifth degree remains. For example, if under a root there is a negative number, then and result will be negative. Extraction of root 5 of degree from positive number gives positive number. Thus, the sign "minus" can be taken out from under the sign of a root.

3. Sometimes to take degree root 5, it is necessary to transform expression. It would seem, +40x^3-80x^2+80x-32 the root cannot be taken from x^5-10x^4 polynom. However by close examination it is possible to make sure that this expression is curtailed in (x-2) ^5 (remember a formula for construction of a binomial in the fifth degree). It is obvious that degree root 5 from (x-2) ^5 is equal (x-2).

4. In programming for finding of a root use a recurrence relation. The principle is based on an initial assumption and further increase in accuracy.

5. Let it is required to write the program for extraction of a root of the fifth degree from number A. Set an initial assumption of x0. Further set recurrent formula x (i+1) =1/5 [4x (i)+A/x(i) ^4]. Repeat this step until the required accuracy is reached. Repetition is implemented due to addition of unit to index i.

Author: «MirrorInfo» Dream Team