Solve frac{38-sqrt{38*34}}{2}

$$\frac{ 38- \sqrt{ 38 \times 34 } }{ 2 }$$

Evaluate

$$19-\sqrt{323}\approx 1.027799244$$

Solution Steps

Multiply 38 and 34 to get 1292.

$$\frac{38-\sqrt{1292}}{2}$$

Factor 1292=2^{2}\times 323. Rewrite the square root of the product \sqrt{2^{2}\times 323} as the product of square roots \sqrt{2^{2}}\sqrt{323}. Take the square root of 2^{2}.

$$\frac{38-2\sqrt{323}}{2}$$

Divide each term of 38-2\sqrt{323} by 2 to get 19-\sqrt{323}.

$$19-\sqrt{323}$$