Solve 027*sqrt{95*10^-6*(3000-1205)*981/1205*513^06}=

$$027 \times \sqrt{ \frac{ 95 \times { 10 }^{ -6 } \times (3000-1205) \times 981 }{ 1205 } \times { 513 }^{ 06 } } =$$

Evaluate

$$0$$

Solution Steps

Multiply 0 and 27 to get 0.

$$0\sqrt{\frac{95\times 10^{-6}\left(3000-1205\right)\times 981}{1205}\times 513^{0\times 6}}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$0\sqrt{\frac{95\times \frac{1}{1000000}\left(3000-1205\right)\times 981}{1205}\times 513^{0\times 6}}$$

Multiply 95 and \frac{1}{1000000} to get \frac{19}{200000}.

$$0\sqrt{\frac{\frac{19}{200000}\left(3000-1205\right)\times 981}{1205}\times 513^{0\times 6}}$$

Subtract 1205 from 3000 to get 1795.

$$0\sqrt{\frac{\frac{19}{200000}\times 1795\times 981}{1205}\times 513^{0\times 6}}$$

Multiply \frac{19}{200000} and 1795 to get \frac{6821}{40000}.

$$0\sqrt{\frac{\frac{6821}{40000}\times 981}{1205}\times 513^{0\times 6}}$$

Multiply \frac{6821}{40000} and 981 to get \frac{6691401}{40000}.

$$0\sqrt{\frac{\frac{6691401}{40000}}{1205}\times 513^{0\times 6}}$$

Express \frac{\frac{6691401}{40000}}{1205} as a single fraction.

$$0\sqrt{\frac{6691401}{40000\times 1205}\times 513^{0\times 6}}$$

Multiply 40000 and 1205 to get 48200000.

$$0\sqrt{\frac{6691401}{48200000}\times 513^{0\times 6}}$$

Multiply 0 and 6 to get 0.

$$0\sqrt{\frac{6691401}{48200000}\times 513^{0}}$$

Calculate 513 to the power of 0 and get 1.

$$0\sqrt{\frac{6691401}{48200000}\times 1}$$

Multiply \frac{6691401}{48200000} and 1 to get \frac{6691401}{48200000}.

$$0\sqrt{\frac{6691401}{48200000}}$$

Rewrite the square root of the division \sqrt{\frac{6691401}{48200000}} as the division of square roots \frac{\sqrt{6691401}}{\sqrt{48200000}}.

$$0\times \frac{\sqrt{6691401}}{\sqrt{48200000}}$$

Factor 6691401=3^{2}\times 743489. Rewrite the square root of the product \sqrt{3^{2}\times 743489} as the product of square roots \sqrt{3^{2}}\sqrt{743489}. Take the square root of 3^{2}.

$$0\times \frac{3\sqrt{743489}}{\sqrt{48200000}}$$

Factor 48200000=200^{2}\times 1205. Rewrite the square root of the product \sqrt{200^{2}\times 1205} as the product of square roots \sqrt{200^{2}}\sqrt{1205}. Take the square root of 200^{2}.

$$0\times \frac{3\sqrt{743489}}{200\sqrt{1205}}$$

Rationalize the denominator of \frac{3\sqrt{743489}}{200\sqrt{1205}} by multiplying numerator and denominator by \sqrt{1205}.

$$0\times \frac{3\sqrt{743489}\sqrt{1205}}{200\left(\sqrt{1205}\right)^{2}}$$

The square of \sqrt{1205} is 1205.

$$0\times \frac{3\sqrt{743489}\sqrt{1205}}{200\times 1205}$$

To multiply \sqrt{743489} and \sqrt{1205}, multiply the numbers under the square root.

$$0\times \frac{3\sqrt{895904245}}{200\times 1205}$$

Multiply 200 and 1205 to get 241000.

$$0\times \frac{3\sqrt{895904245}}{241000}$$

Anything times zero gives zero.

$$0$$

Factor

$$0$$