Solve frac{0.77*4.4*10^6*0.126+sqrt{left(0.77^2-0.30right)4.4^210^12*{0.126}^2+4*4.4*{10}^6*25000*0.126}}{4.4{10}^6}

$$\frac{ 0.77 \cdot 4.4 \times { 10 }^{ 6 } \times 0.126+ \sqrt{ \left( { 0.77 }^{ 2 } -0.30 \right) { 4.4 }^{ 2 } { 10 }^{ 12 } \times { 0.126 }^{ 2 } +4 \cdot 4.4 \times { 10 }^{ 6 } \times 25000 \cdot 0.126 } }{ 4.4 { 10 }^{ 6 } }$$

Evaluate

$$\frac{3\left(\sqrt{252544369}+17787\right)}{550000}\approx 0.183701698$$

Solution Steps

Multiply 0.77 and 4.4 to get 3.388.

$$\frac{3.388\times 10^{6}\times 0.126+\sqrt{\left(0.77^{2}-0.3\right)\times 4.4^{2}\times 10^{12}\times 0.126^{2}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{3.388\times 1000000\times 0.126+\sqrt{\left(0.77^{2}-0.3\right)\times 4.4^{2}\times 10^{12}\times 0.126^{2}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 3.388 and 1000000 to get 3388000.

$$\frac{3388000\times 0.126+\sqrt{\left(0.77^{2}-0.3\right)\times 4.4^{2}\times 10^{12}\times 0.126^{2}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 3388000 and 0.126 to get 426888.

$$\frac{426888+\sqrt{\left(0.77^{2}-0.3\right)\times 4.4^{2}\times 10^{12}\times 0.126^{2}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Calculate 0.77 to the power of 2 and get 0.5929.

$$\frac{426888+\sqrt{\left(0.5929-0.3\right)\times 4.4^{2}\times 10^{12}\times 0.126^{2}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Subtract 0.3 from 0.5929 to get 0.2929.

$$\frac{426888+\sqrt{0.2929\times 4.4^{2}\times 10^{12}\times 0.126^{2}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Calculate 4.4 to the power of 2 and get 19.36.

$$\frac{426888+\sqrt{0.2929\times 19.36\times 10^{12}\times 0.126^{2}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 0.2929 and 19.36 to get 5.670544.

$$\frac{426888+\sqrt{5.670544\times 10^{12}\times 0.126^{2}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\frac{426888+\sqrt{5.670544\times 1000000000000\times 0.126^{2}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 5.670544 and 1000000000000 to get 5670544000000.

$$\frac{426888+\sqrt{5670544000000\times 0.126^{2}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Calculate 0.126 to the power of 2 and get 0.015876.

$$\frac{426888+\sqrt{5670544000000\times 0.015876+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 5670544000000 and 0.015876 to get 90025556544.

$$\frac{426888+\sqrt{90025556544+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 4 and 4.4 to get 17.6.

$$\frac{426888+\sqrt{90025556544+17.6\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{426888+\sqrt{90025556544+17.6\times 1000000\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 17.6 and 1000000 to get 17600000.

$$\frac{426888+\sqrt{90025556544+17600000\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 17600000 and 25000 to get 440000000000.

$$\frac{426888+\sqrt{90025556544+440000000000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 440000000000 and 0.126 to get 55440000000.

$$\frac{426888+\sqrt{90025556544+55440000000}}{4.4\times 10^{6}}$$

Add 90025556544 and 55440000000 to get 145465556544.

$$\frac{426888+\sqrt{145465556544}}{4.4\times 10^{6}}$$

Factor 145465556544=24^{2}\times 252544369. Rewrite the square root of the product \sqrt{24^{2}\times 252544369} as the product of square roots \sqrt{24^{2}}\sqrt{252544369}. Take the square root of 24^{2}.

$$\frac{426888+24\sqrt{252544369}}{4.4\times 10^{6}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{426888+24\sqrt{252544369}}{4.4\times 1000000}$$

Multiply 4.4 and 1000000 to get 4400000.

$$\frac{426888+24\sqrt{252544369}}{4400000}$$