Solve sqrt{0.804*0.881/left(0.804+0.881right)^2}

$$\sqrt{ \frac{ 0.804 \times 0.881 }{ { \left(0.804+0.881 \right) }^{ 2 } } }$$

Evaluate

$$\frac{2\sqrt{177081}}{1685}\approx 0.499477666$$

Solution Steps

Multiply 0.804 and 0.881 to get 0.708324.

$$\sqrt{\frac{0.708324}{\left(0.804+0.881\right)^{2}}}$$

Add 0.804 and 0.881 to get 1.685.

$$\sqrt{\frac{0.708324}{1.685^{2}}}$$

Calculate 1.685 to the power of 2 and get 2.839225.

$$\sqrt{\frac{0.708324}{2.839225}}$$

Expand \frac{0.708324}{2.839225} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{708324}{2839225}}$$

Rewrite the square root of the division \sqrt{\frac{708324}{2839225}} as the division of square roots \frac{\sqrt{708324}}{\sqrt{2839225}}.

$$\frac{\sqrt{708324}}{\sqrt{2839225}}$$

Factor 708324=2^{2}\times 177081. Rewrite the square root of the product \sqrt{2^{2}\times 177081} as the product of square roots \sqrt{2^{2}}\sqrt{177081}. Take the square root of 2^{2}.

$$\frac{2\sqrt{177081}}{\sqrt{2839225}}$$

Calculate the square root of 2839225 and get 1685.

$$\frac{2\sqrt{177081}}{1685}$$