Mister Exam

Other calculators

How do you sqrt((x^4+16*y^2)/(4*x^2)) in partial fractions?

An expression to simplify:

The solution

You have entered [src]
      ____________
     /  4       2 
    /  x  + 16*y  
   /   ---------- 
  /          2    
\/        4*x     
$$\sqrt{\frac{x^{4} + 16 y^{2}}{4 x^{2}}}$$
sqrt((x^4 + 16*y^2)/((4*x^2)))
Fraction decomposition [src]
sqrt(x^2/4 + 4*y^2/x^2)
$$\sqrt{\frac{x^{2}}{4} + \frac{4 y^{2}}{x^{2}}}$$
      ___________
     /  2      2 
    /  x    4*y  
   /   -- + ---- 
  /    4      2  
\/           x   
General simplification [src]
      ____________
     /  4       2 
    /  x  + 16*y  
   /   ---------- 
  /         2     
\/         x      
------------------
        2         
$$\frac{\sqrt{\frac{x^{4} + 16 y^{2}}{x^{2}}}}{2}$$
sqrt((x^4 + 16*y^2)/x^2)/2
Numerical answer [src]
0.5*((x^4 + 16.0*y^2)/x^2)^0.5
0.5*((x^4 + 16.0*y^2)/x^2)^0.5
Powers [src]
        ___________
       /         4 
      /     2   x  
     /   4*y  + -- 
    /           4  
   /     --------- 
  /           2    
\/           x     
$$\sqrt{\frac{\frac{x^{4}}{4} + 4 y^{2}}{x^{2}}}$$
      ____________
     /  4       2 
    /  x  + 16*y  
   /   ---------- 
  /         2     
\/         x      
------------------
        2         
$$\frac{\sqrt{\frac{x^{4} + 16 y^{2}}{x^{2}}}}{2}$$
sqrt((x^4 + 16*y^2)/x^2)/2
Rational denominator [src]
      ____________
     /  4       2 
    /  x  + 16*y  
   /   ---------- 
  /         2     
\/         x      
------------------
        2         
$$\frac{\sqrt{\frac{x^{4} + 16 y^{2}}{x^{2}}}}{2}$$
sqrt((x^4 + 16*y^2)/x^2)/2
Assemble expression [src]
      ____________
     /  4       2 
    /  x  + 16*y  
   /   ---------- 
  /         2     
\/         x      
------------------
        2         
$$\frac{\sqrt{\frac{x^{4} + 16 y^{2}}{x^{2}}}}{2}$$
sqrt((x^4 + 16*y^2)/x^2)/2
Expand expression [src]
      ____________
     /  4       2 
    /  x  + 16*y  
   /   ---------- 
  /         2     
\/         x      
------------------
        2         
$$\frac{\sqrt{\frac{x^{4} + 16 y^{2}}{x^{2}}}}{2}$$
sqrt((x^4 + 16*y^2)/x^2)/2
Common denominator [src]
      ____________
     /          2 
    /   2   16*y  
   /   x  + ----- 
  /            2  
\/            x   
------------------
        2         
$$\frac{\sqrt{x^{2} + \frac{16 y^{2}}{x^{2}}}}{2}$$
sqrt(x^2 + 16*y^2/x^2)/2
Trigonometric part [src]
      ____________
     /  4       2 
    /  x  + 16*y  
   /   ---------- 
  /         2     
\/         x      
------------------
        2         
$$\frac{\sqrt{\frac{x^{4} + 16 y^{2}}{x^{2}}}}{2}$$
sqrt((x^4 + 16*y^2)/x^2)/2
Combining rational expressions [src]
      ____________
     /  4       2 
    /  x  + 16*y  
   /   ---------- 
  /         2     
\/         x      
------------------
        2         
$$\frac{\sqrt{\frac{x^{4} + 16 y^{2}}{x^{2}}}}{2}$$
sqrt((x^4 + 16*y^2)/x^2)/2
Combinatorics [src]
      ____________
     /          2 
    /   2   16*y  
   /   x  + ----- 
  /            2  
\/            x   
------------------
        2         
$$\frac{\sqrt{x^{2} + \frac{16 y^{2}}{x^{2}}}}{2}$$
sqrt(x^2 + 16*y^2/x^2)/2