Solve frac{0.615*4.4*10^6*0.126+sqrt{(0.615^2-0.088)*4.4^2*10^12+4*4.4*{10}^6*25000*0.126}}{4.4*{10}^6}

$$\frac{ 0.615 \times 4.4 \times { 10 }^{ 6 } \times 0.126+ \sqrt{ ( { 0.615 }^{ 2 } -0.088) \times { 4.4 }^{ 2 } \times { 10 }^{ 12 } +4 \times 4.4 \times { 10 }^{ 6 } \times 25000 \times 0.126 } }{ 4.4 \times { 10 }^{ 6 } }$$

Evaluate

$$\frac{\sqrt{1418549}}{2200}+0.07749\approx 0.618866612$$

Solution Steps

Multiply 0.615 and 4.4 to get 2.706.

$$\frac{2.706\times 10^{6}\times 0.126+\sqrt{\left(0.615^{2}-0.088\right)\times 4.4^{2}\times 10^{12}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{2.706\times 1000000\times 0.126+\sqrt{\left(0.615^{2}-0.088\right)\times 4.4^{2}\times 10^{12}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 2.706 and 1000000 to get 2706000.

$$\frac{2706000\times 0.126+\sqrt{\left(0.615^{2}-0.088\right)\times 4.4^{2}\times 10^{12}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 2706000 and 0.126 to get 340956.

$$\frac{340956+\sqrt{\left(0.615^{2}-0.088\right)\times 4.4^{2}\times 10^{12}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Calculate 0.615 to the power of 2 and get 0.378225.

$$\frac{340956+\sqrt{\left(0.378225-0.088\right)\times 4.4^{2}\times 10^{12}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Subtract 0.088 from 0.378225 to get 0.290225.

$$\frac{340956+\sqrt{0.290225\times 4.4^{2}\times 10^{12}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Calculate 4.4 to the power of 2 and get 19.36.

$$\frac{340956+\sqrt{0.290225\times 19.36\times 10^{12}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 0.290225 and 19.36 to get 5.618756.

$$\frac{340956+\sqrt{5.618756\times 10^{12}+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\frac{340956+\sqrt{5.618756\times 1000000000000+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 5.618756 and 1000000000000 to get 5618756000000.

$$\frac{340956+\sqrt{5618756000000+4\times 4.4\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 4 and 4.4 to get 17.6.

$$\frac{340956+\sqrt{5618756000000+17.6\times 10^{6}\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{340956+\sqrt{5618756000000+17.6\times 1000000\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 17.6 and 1000000 to get 17600000.

$$\frac{340956+\sqrt{5618756000000+17600000\times 25000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 17600000 and 25000 to get 440000000000.

$$\frac{340956+\sqrt{5618756000000+440000000000\times 0.126}}{4.4\times 10^{6}}$$

Multiply 440000000000 and 0.126 to get 55440000000.

$$\frac{340956+\sqrt{5618756000000+55440000000}}{4.4\times 10^{6}}$$

Add 5618756000000 and 55440000000 to get 5674196000000.

$$\frac{340956+\sqrt{5674196000000}}{4.4\times 10^{6}}$$

Factor 5674196000000=2000^{2}\times 1418549. Rewrite the square root of the product \sqrt{2000^{2}\times 1418549} as the product of square roots \sqrt{2000^{2}}\sqrt{1418549}. Take the square root of 2000^{2}.

$$\frac{340956+2000\sqrt{1418549}}{4.4\times 10^{6}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{340956+2000\sqrt{1418549}}{4.4\times 1000000}$$

Multiply 4.4 and 1000000 to get 4400000.

$$\frac{340956+2000\sqrt{1418549}}{4400000}$$