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¿Cómo vas a descomponer esta sqrt((49/50-x^2/(193/2)^2)*71²) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
      ____________________
     / /        2  \      
    /  |49     x   |      
   /   |-- - ------|*5041 
  /    |50        2|      
\/     \     193/2 /      
$$\sqrt{5041 \left(- \frac{x^{2}}{\left(\frac{193}{2}\right)^{2}} + \frac{49}{50}\right)}$$
sqrt((49/50 - x^2/(193/2)^2)*5041)
Descomposición de una fracción [src]
sqrt(2)*sqrt(9200838241 - 1008200*x^2)/1930
$$\frac{\sqrt{2} \sqrt{9200838241 - 1008200 x^{2}}}{1930}$$
         _________________________
  ___   /                       2 
\/ 2 *\/  9200838241 - 1008200*x  
----------------------------------
               1930               
Simplificación general [src]
      __________________
     /                2 
71*\/  3650402 - 400*x  
------------------------
          1930          
$$\frac{71 \sqrt{3650402 - 400 x^{2}}}{1930}$$
71*sqrt(3650402 - 400*x^2)/1930
Respuesta numérica [src]
70.2864140499428*(1 - 0.000109576972618358*x^2)^0.5
70.2864140499428*(1 - 0.000109576972618358*x^2)^0.5
Abrimos la expresión [src]
         _____________
        /         2   
       /  49     x    
71*   /   -- - ------ 
     /    50        2 
   \/          193/2  
$$71 \sqrt{- \frac{x^{2}}{\left(\frac{193}{2}\right)^{2}} + \frac{49}{50}}$$
71*sqrt(49/50 - x^2/(193/2)^2)
Parte trigonométrica [src]
     ___________________
    /                 2 
   /  247009   20164*x  
  /   ------ - -------- 
\/      50      37249   
$$\sqrt{\frac{247009}{50} - \frac{20164 x^{2}}{37249}}$$
sqrt(247009/50 - 20164*x^2/37249)
Potencias [src]
     ___________________
    /                 2 
   /  247009   20164*x  
  /   ------ - -------- 
\/      50      37249   
$$\sqrt{\frac{247009}{50} - \frac{20164 x^{2}}{37249}}$$
sqrt(247009/50 - 20164*x^2/37249)
Denominador común [src]
            __________________
     ___   /                2 
71*\/ 2 *\/  1825201 - 200*x  
------------------------------
             1930             
$$\frac{71 \sqrt{2} \sqrt{1825201 - 200 x^{2}}}{1930}$$
71*sqrt(2)*sqrt(1825201 - 200*x^2)/1930
Compilar la expresión [src]
     ___________________
    /                 2 
   /  247009   20164*x  
  /   ------ - -------- 
\/      50      37249   
$$\sqrt{\frac{247009}{50} - \frac{20164 x^{2}}{37249}}$$
sqrt(247009/50 - 20164*x^2/37249)
Denominador racional [src]
         _________________________
  ___   /                       2 
\/ 2 *\/  9200838241 - 1008200*x  
----------------------------------
               1930               
$$\frac{\sqrt{2} \sqrt{9200838241 - 1008200 x^{2}}}{1930}$$
sqrt(2)*sqrt(9200838241 - 1008200*x^2)/1930
Combinatoria [src]
            __________________
     ___   /                2 
71*\/ 2 *\/  1825201 - 200*x  
------------------------------
             1930             
$$\frac{71 \sqrt{2} \sqrt{1825201 - 200 x^{2}}}{1930}$$
71*sqrt(2)*sqrt(1825201 - 200*x^2)/1930
Unión de expresiones racionales [src]
            __________________
     ___   /                2 
71*\/ 2 *\/  1825201 - 200*x  
------------------------------
             1930             
$$\frac{71 \sqrt{2} \sqrt{1825201 - 200 x^{2}}}{1930}$$
71*sqrt(2)*sqrt(1825201 - 200*x^2)/1930