Solve sqrt{0.804*0.728/left(0.804+0.758right)^2}

$$\sqrt{ \frac{ 0.804 \times 0.728 }{ { \left(0.804+0.758 \right) }^{ 2 } } }$$

Evaluate

$$\frac{2\sqrt{36582}}{781}\approx 0.489793125$$

Solution Steps

Multiply 0.804 and 0.728 to get 0.585312.

$$\sqrt{\frac{0.585312}{\left(0.804+0.758\right)^{2}}}$$

Add 0.804 and 0.758 to get 1.562.

$$\sqrt{\frac{0.585312}{1.562^{2}}}$$

Calculate 1.562 to the power of 2 and get 2.439844.

$$\sqrt{\frac{0.585312}{2.439844}}$$

Expand \frac{0.585312}{2.439844} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{585312}{2439844}}$$

Reduce the fraction \frac{585312}{2439844} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{146328}{609961}}$$

Rewrite the square root of the division \sqrt{\frac{146328}{609961}} as the division of square roots \frac{\sqrt{146328}}{\sqrt{609961}}.

$$\frac{\sqrt{146328}}{\sqrt{609961}}$$

Factor 146328=2^{2}\times 36582. Rewrite the square root of the product \sqrt{2^{2}\times 36582} as the product of square roots \sqrt{2^{2}}\sqrt{36582}. Take the square root of 2^{2}.

$$\frac{2\sqrt{36582}}{\sqrt{609961}}$$

Calculate the square root of 609961 and get 781.

$$\frac{2\sqrt{36582}}{781}$$