Any root solver

[prog_tom]

	static double PowerDec(double x, double a){
		//Evaluates decimal powers from i+0.01 -> i+0.99
		double b = 0;//value of the root.
		int i = 0; 
		//Check special cases
		if (a == 1)
		return x;
		
		//Check power if > 1.
		while (a > 1) {
			a -= 1;
			i += 1;
		}

	
		//MAIN		
		
		if( (a>=0.01) && (a<0.125)  ){ //0.11 1/9
			while ((b*b*b*b*b*b*b*b*b) <= x) {
				b += 0.0001;
			}
		}				
		if( (a>=0.125) && (a<0.14)  ){ //0.125 1/8
			while ((b*b*b*b*b*b*b*b) <= x) {
				b += 0.0001;
			}
		}				
		if( (a>=0.16) && (a<=0.17)  ){ //0.16 1/6
			while ((b*b*b*b*b*b) <= x) {
				b += 0.0001;
			}
		}		
		if( (a>=0.14) && (a<0.17)  ){ //0.14 1/7
			while ((b*b*b*b*b*b*b) <= x) {
				b += 0.0001;
			}
		}
		if( (a>0.17) && (a<0.25) ){ //0.2
			while ((b*b*b*b*b) <= x) {
				b += 0.0001;
			}
		}
		if( (a>=0.25) && (a<0.3) ) {//0.25
			while ((b*b*b*b) <= x) {
				b += 0.0001;
			}
		}
		if( (a>=0.3) && (a<0.45) ) {//0.3
			while ((b*b*b) <= x) {
				b += 0.0001;
			}
		}
		if( (a>=0.45) && (a<0.55) ) {//0.5, just call sqrt
			b=Sqrt(x);
		}
		if( (a>=0.55) && (a<0.65) ) {//0.6, 3/5
			while ((b*b*b*b*b) <= (x*x*x)) {
				b += 0.0001;
			}
		}
		if( (a>=0.65) && (a<0.75) ) {//0.7, 7/10
			while ((b*b*b*b*b*b*b*b*b*b) <= (x*x*x*x*x*x*x)) {
				b += 0.0001;
			}
		}
		if( (a>=0.75) && (a<0.85) ) {//0.8, 4/5
			while ((b*b*b*b*b) <= (x*x*x*x)) {
				b += 0.0001;
			}
		}
		if( (a>=0.85) && (a<=0.99) ) {//0.9, 9/10
			while ((b*b*b*b*b*b*b*b*b*b) <= (x*x*x*x*x*x*x*x*x)) {
				b += 0.0001;
			}
		}		
					
		//Check if i>=1, multiply b by x i times until i becomes less than 1. 
		//IE x^(1.2) = x^1 * x^0.2 
		while (i>=1) {
			b *= x;
		    i -= 1;
		}
		return b;
	}

Please leave your comments thanks.

[CornedBee]

See the C++ version.

Why are you trying to recreate all the stuff from java.lang.Math? You really only learn about maths this way, and not so much about the language.