Solve .5-(10*5)^2/2*1/sqrt{2}

$$.5 - \frac { ( 10 \cdot 5 ) ^ { 2 } } { 2 } \times \frac { 1 } { \sqrt { 2 } }$$

Evaluate

$$0.5-625\sqrt{2}\approx -883.383476483$$

Solution Steps

Multiply 10 and 5 to get 50.

$$0.5-\frac{50^{2}}{2}\times \frac{1}{\sqrt{2}}$$

Calculate 50 to the power of 2 and get 2500.

$$0.5-\frac{2500}{2}\times \frac{1}{\sqrt{2}}$$

Divide 2500 by 2 to get 1250.

$$0.5-1250\times \frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$0.5-1250\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$0.5-1250\times \frac{\sqrt{2}}{2}$$

Cancel out 2, the greatest common factor in 1250 and 2.

$$0.5-625\sqrt{2}$$

Factor

$$0.5-625\sqrt{2}$$