Solve frac{3sqrt{-17+45865}}{188^2}

$$\frac{ 3 \sqrt{ -17+45865 } }{ { 188 }^{ 2 } }$$

Evaluate

$$\frac{3\sqrt{11462}}{17672}\approx 0.018174637$$

Solution Steps

Add -17 and 45865 to get 45848.

$$\frac{3\sqrt{45848}}{188^{2}}$$

Factor 45848=2^{2}\times 11462. Rewrite the square root of the product \sqrt{2^{2}\times 11462} as the product of square roots \sqrt{2^{2}}\sqrt{11462}. Take the square root of 2^{2}.

$$\frac{3\times 2\sqrt{11462}}{188^{2}}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{11462}}{188^{2}}$$

Calculate 188 to the power of 2 and get 35344.

$$\frac{6\sqrt{11462}}{35344}$$

Divide 6\sqrt{11462} by 35344 to get \frac{3}{17672}\sqrt{11462}.

$$\frac{3}{17672}\sqrt{11462}$$