The number which is under the sign of a root often disturbs the solution of the equation, it is inconvenient to work with it. Even if it is built in degree, fractionally or cannot be presented in the integer form to some extent, it is possible to try to bring him out of a root, completely or at least partially.
Instruction
1. Try to spread out number to simple multipliers. If number fractional, do not consider a comma so far, consider all figures. For example, number 8.91 can be spread out so: 8.91=0.9*0.9*11 (at first spread out 891=9*9*11, then add commas). Now you can write down number as 0.9^2*11 and to bring out of root 0.9. Thus, you received √8,91=0,9√11.
2. If you were given a cubic root, it is necessary to remove under it number in the third degree. For example, spread out number 135 as 3*3*3*5=3^3*5. Bring number 3 out of a root, number 5 at the same time will remain under the sign of a root. Do the same with roots of the fourth and higher degree.
3. To bring out of a root number with the degree other than root degree (for example, a root square, and under it number in 3 degrees), act this way. Write down a root as degree, that is remove the sign √ and put instead of it the sign of degree. For example, the square root from number is equal to the same number in degree ½, and cubic – in degree 1/3. Do not forget to bracket a radicand at the same time.
4. Simplify expression, having multiplied degrees. For example, if under a root there was number 12^4, and the root was square, expression will take a form (12^4) ^1/2=12^4/2=12^2=144.
5. It is possible to bring out of the sign of a root also a negative number. If degree odd, just present number under a root as number in the same degree, for example,-8=(-2) ^3, the cubic root from (-8) will be equal (-2).
6. To take out a negative number from under a root of even degree (including square), arrive thus. Present a radicand in the form of the work (-1) and number in the necessary degree, then take out number, having left (-1) under the sign of a root. For example, √ (-144)= √ (-1) * √144=12 * √ (-1). At the same time √ in mathematics it is accepted to call number (-1) imaginary number and to designate by parameter i. Thus, √ (-144) =12i.