Root from number x is called such number which at exponentiation of a root will be equal x. A multiplier is called the multiplied number. That is, in expression of a look h*zhu it is necessary to bring x at the roots.
Instruction
1. Define root degree. It is usually designated by nadstrochny figure before it. If degree of a root is not specified, then a root square, its degree - two.
2. Bring a multiplier at the roots, having built it in root degree. That is h*zhu = √ (u*khzh).
3. Review an example 5 * √ 2. A square root therefore square number 5, that is in the second degree. It will turn out √ (2*5²). Simplify a radicand. √ (2*5²) = √ (2*25) = √50.
4. Study an example 2*³ √ (7+x). In this case a cube root therefore build the multiplier which is out of a root in the 3rd degree. It will turn out³ √ (7+x) *2³) =³ √ (7+x) *8).
5. Review an example (2/9) * √ (7+x) where it is necessary to bring at the roots fraction. The algorithm of actions almost does not differ. Build numerator and a denominator of fraction in degree. It will turn out √ ((7+x) * (2²/9²)). Simplify a radicand if it is necessary.
6. Solve one more example in which the multiplier already has a degree. In y² * √ (x³) the multiplier brought at the roots is squared. At construction in new degree and introduction at the roots degrees are just multiplied. That is, after introduction under a square root, y² will have I quarter degree.
7. Review an example in which degree is fraction, that is the multiplier also is under a root. Find in an example √ (y³)*³ √ (x) degrees x and y. Degree x is equal 1/3, that is the cube root, and the multiplier of y brought at the roots has degree 3/2, that is it cubed and under a square root.
8. Lead roots to one degree to connect radicands. For this purpose lead fractions of degrees to a uniform denominator. Increase numerator and a denominator of fraction by the same number which will allow to achieve it.
9. Find a common denominator for fractions of degrees. For 1/3 and 3/2 it there will be 6. Increase both part one of fraction by two, and the second by three. That is (1*2)/(3*2) and (3*3)/(2*3). 2/6 and 9/6 will turn out, respectively. Thus, x and y will be under the general root of the sixth degree, x in the second, and y in the ninth degree.