Solve 1000*40/sqrt{35*10}*150

$$1000 \times \frac { 40 } { \sqrt { 35 } \times 10 } \times 150$$

Evaluate

$$\frac{120000\sqrt{35}}{7}\approx 101418.510567422$$

Solution Steps

Multiply 150 and 1000 to get 150000.

$$150000\times \frac{40}{10\sqrt{35}}$$

Rationalize the denominator of \frac{40}{10\sqrt{35}} by multiplying numerator and denominator by \sqrt{35}.

$$150000\times \frac{40\sqrt{35}}{10\left(\sqrt{35}\right)^{2}}$$

The square of \sqrt{35} is 35.

$$150000\times \frac{40\sqrt{35}}{10\times 35}$$

Cancel out 10 in both numerator and denominator.

$$150000\times \frac{4\sqrt{35}}{35}$$

Express 150000\times \frac{4\sqrt{35}}{35} as a single fraction.

$$\frac{150000\times 4\sqrt{35}}{35}$$

Multiply 150000 and 4 to get 600000.

$$\frac{600000\sqrt{35}}{35}$$

Divide 600000\sqrt{35} by 35 to get \frac{120000}{7}\sqrt{35}.

$$\frac{120000}{7}\sqrt{35}$$