Solve frac{(1+2+3)!+e*1^2+sqrt{10^2}-1}{2}+1n8

$$\frac { ( 1 + 2 + 3 ) ! + e \times 1 ^ { 2 } + \sqrt { 10 ^ { 2 } } - 1 } { 2 } + 1 n 8$$

Evaluate

$$n_{8}+\frac{e}{2}+\frac{729}{2}$$

Short Solution Steps

Add 1 and 2 to get 3.

$$\frac{\left(3+3\right)!+e\times 1^{2}+\sqrt{10^{2}}-1}{2}+1n_{8}$$

Add 3 and 3 to get 6.

$$\frac{6!+e\times 1^{2}+\sqrt{10^{2}}-1}{2}+1n_{8}$$

The factorial of 6 is 720.

$$\frac{720+e\times 1^{2}+\sqrt{10^{2}}-1}{2}+1n_{8}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{720+e\times 1+\sqrt{10^{2}}-1}{2}+1n_{8}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{720+e\times 1+\sqrt{100}-1}{2}+1n_{8}$$

Calculate the square root of 100 and get 10.

$$\frac{720+e\times 1+10-1}{2}+1n_{8}$$

Add 720 and 10 to get 730.

$$\frac{730+e\times 1-1}{2}+1n_{8}$$

Subtract 1 from 730 to get 729.

$$\frac{729+e\times 1}{2}+1n_{8}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1n_{8} times \frac{2}{2}.

$$\frac{729+e\times 1}{2}+\frac{2\times 1n_{8}}{2}$$

Since \frac{729+e\times 1}{2} and \frac{2\times 1n_{8}}{2} have the same denominator, add them by adding their numerators.

$$\frac{729+e\times 1+2\times 1n_{8}}{2}$$

Do the multiplications in 729+e\times 1+2\times 1n_{8}.

$$\frac{729+e+2n_{8}}{2}$$

Factor

$$\frac{2n_{8}+e+729}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{729+e+2n_{8}}{2}$$