Solve 1000*0.535*sqrt{0.03^2/0.03^2+0.01^2}

$$1000 \times 0.535 \times \sqrt{ \frac{ { 0.03 }^{ 2 } }{ { 0.03 }^{ 2 } + { 0.01 }^{ 2 } } }$$

Evaluate

$$\frac{321\sqrt{1000}}{20}\approx 507.545564457$$

Solution Steps

Multiply 0.535 and 1000 to get 535.

$$535\sqrt{\frac{0.03^{2}}{0.03^{2}+0.01^{2}}}$$

Calculate 0.03 to the power of 2 and get 0.0009.

$$535\sqrt{\frac{0.0009}{0.03^{2}+0.01^{2}}}$$

Calculate 0.03 to the power of 2 and get 0.0009.

$$535\sqrt{\frac{0.0009}{0.0009+0.01^{2}}}$$

Calculate 0.01 to the power of 2 and get 0.0001.

$$535\sqrt{\frac{0.0009}{0.0009+0.0001}}$$

Add 0.0009 and 0.0001 to get 0.001.

$$535\sqrt{\frac{0.0009}{0.001}}$$

Expand \frac{0.0009}{0.001} by multiplying both numerator and the denominator by 10000.

$$535\sqrt{\frac{9}{10}}$$

Rewrite the square root of the division \sqrt{\frac{9}{10}} as the division of square roots \frac{\sqrt{9}}{\sqrt{10}}.

$$535\times \frac{\sqrt{9}}{\sqrt{10}}$$

Calculate the square root of 9 and get 3.

$$535\times \frac{3}{\sqrt{10}}$$

Rationalize the denominator of \frac{3}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$535\times \frac{3\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$535\times \frac{3\sqrt{10}}{10}$$

Express 535\times \frac{3\sqrt{10}}{10} as a single fraction.

$$\frac{535\times 3\sqrt{10}}{10}$$

Multiply 535 and 3 to get 1605.

$$\frac{1605\sqrt{10}}{10}$$

Divide 1605\sqrt{10} by 10 to get \frac{321}{2}\sqrt{10}.

$$\frac{321}{2}\sqrt{10}$$