Solve sqrt{0.804*0.988/left(0.804+0.988right)^2}

$$\sqrt{ \frac{ 0.804 \times 0.988 }{ { \left(0.804+0.988 \right) }^{ 2 } } }$$

Evaluate

$$\frac{\sqrt{49647}}{448}\approx 0.497357294$$

Solution Steps

Multiply 0.804 and 0.988 to get 0.794352.

$$\sqrt{\frac{0.794352}{\left(0.804+0.988\right)^{2}}}$$

Add 0.804 and 0.988 to get 1.792.

$$\sqrt{\frac{0.794352}{1.792^{2}}}$$

Calculate 1.792 to the power of 2 and get 3.211264.

$$\sqrt{\frac{0.794352}{3.211264}}$$

Expand \frac{0.794352}{3.211264} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{794352}{3211264}}$$

Reduce the fraction \frac{794352}{3211264} to lowest terms by extracting and canceling out 16.

$$\sqrt{\frac{49647}{200704}}$$

Rewrite the square root of the division \sqrt{\frac{49647}{200704}} as the division of square roots \frac{\sqrt{49647}}{\sqrt{200704}}.

$$\frac{\sqrt{49647}}{\sqrt{200704}}$$

Calculate the square root of 200704 and get 448.

$$\frac{\sqrt{49647}}{448}$$