Solve 1div2div3.14div100*sqrt{{left(13.36/0.1right)}^2-1.8^2}

$$1 \div 2 \div 3.14 \div 100 \times \sqrt{ { \left( \frac{ 13.36 }{ 0.1 } \right) }^{ 2 } - { 1.8 }^{ 2 } }$$

Evaluate

$$\frac{\sqrt{446143}}{3140}\approx 0.212719544$$

Solution Steps

Express \frac{\frac{\frac{1}{2}}{3.14}}{100} as a single fraction.

$$\frac{\frac{1}{2}}{3.14\times 100}\sqrt{\left(\frac{13.36}{0.1}\right)^{2}-1.8^{2}}$$

Multiply 3.14 and 100 to get 314.

$$\frac{\frac{1}{2}}{314}\sqrt{\left(\frac{13.36}{0.1}\right)^{2}-1.8^{2}}$$

Express \frac{\frac{1}{2}}{314} as a single fraction.

$$\frac{1}{2\times 314}\sqrt{\left(\frac{13.36}{0.1}\right)^{2}-1.8^{2}}$$

Multiply 2 and 314 to get 628.

$$\frac{1}{628}\sqrt{\left(\frac{13.36}{0.1}\right)^{2}-1.8^{2}}$$

Expand \frac{13.36}{0.1} by multiplying both numerator and the denominator by 100.

$$\frac{1}{628}\sqrt{\left(\frac{1336}{10}\right)^{2}-1.8^{2}}$$

Reduce the fraction \frac{1336}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{628}\sqrt{\left(\frac{668}{5}\right)^{2}-1.8^{2}}$$

Calculate \frac{668}{5} to the power of 2 and get \frac{446224}{25}.

$$\frac{1}{628}\sqrt{\frac{446224}{25}-1.8^{2}}$$

Calculate 1.8 to the power of 2 and get 3.24.

$$\frac{1}{628}\sqrt{\frac{446224}{25}-3.24}$$

Subtract 3.24 from \frac{446224}{25} to get \frac{446143}{25}.

$$\frac{1}{628}\sqrt{\frac{446143}{25}}$$

Rewrite the square root of the division \sqrt{\frac{446143}{25}} as the division of square roots \frac{\sqrt{446143}}{\sqrt{25}}.

$$\frac{1}{628}\times \frac{\sqrt{446143}}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$\frac{1}{628}\times \frac{\sqrt{446143}}{5}$$

Multiply \frac{1}{628} times \frac{\sqrt{446143}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{446143}}{628\times 5}$$

Multiply 628 and 5 to get 3140.

$$\frac{\sqrt{446143}}{3140}$$