Solve sqrt{(12,5/2)^2+34^2}

$$\sqrt { ( \frac { 12,5 } { 2 } ) ^ { 2 } + 34 ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{19121}}{4}\approx 34.569676018$$

Solution Steps

Expand \frac{12,5}{2} by multiplying both numerator and the denominator by 10.

$$\sqrt{\left(\frac{125}{20}\right)^{2}+34^{2}}$$

Reduce the fraction \frac{125}{20} to lowest terms by extracting and canceling out 5.

$$\sqrt{\left(\frac{25}{4}\right)^{2}+34^{2}}$$

Calculate \frac{25}{4} to the power of 2 and get \frac{625}{16}.

$$\sqrt{\frac{625}{16}+34^{2}}$$

Calculate 34 to the power of 2 and get 1156.

$$\sqrt{\frac{625}{16}+1156}$$

Add \frac{625}{16} and 1156 to get \frac{19121}{16}.

$$\sqrt{\frac{19121}{16}}$$

Rewrite the square root of the division \sqrt{\frac{19121}{16}} as the division of square roots \frac{\sqrt{19121}}{\sqrt{16}}.

$$\frac{\sqrt{19121}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\frac{\sqrt{19121}}{4}$$