Solve 40-6000/frac{150{sqrt{40}}}

$$40- \frac{ 6000 }{ \frac{ 150 }{ \sqrt{ 40 } } }$$

Evaluate

$$40-80\sqrt{10}\approx -212.982212813$$

Solution Steps

Divide 6000 by \frac{150}{\sqrt{40}} by multiplying 6000 by the reciprocal of \frac{150}{\sqrt{40}}.

$$40-\frac{6000\sqrt{40}}{150}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$40-\frac{6000\times 2\sqrt{10}}{150}$$

Multiply 6000 and 2 to get 12000.

$$40-\frac{12000\sqrt{10}}{150}$$

Divide 12000\sqrt{10} by 150 to get 80\sqrt{10}.

$$40-80\sqrt{10}$$

Factor

$$40 {(1 - 2 \sqrt{10})} = -212.982212813$$