Solve frac{0.5*4sqrt{2}}{sqrt{1/64*pi*left(60*10^-3right)^4/left(30*10^-3right)^2*pi}}

$$\frac{ 0.5 \times 4 \sqrt{ 2 } }{ \sqrt{ \frac{ \frac{ 1 }{ 64 } \times \pi \times { \left(60 \times { 10 }^{ -3 } \right) }^{ 4 } }{ { \left(30 \times { 10 }^{ -3 } \right) }^{ 2 } \times \pi } } }$$

Evaluate

$$\frac{400\sqrt{2}}{3}\approx 188.561808316$$

Solution Steps

Multiply 0.5 and 4 to get 2.

$$\frac{2\sqrt{2}}{\sqrt{\frac{\frac{1}{64}\pi \times \left(60\times 10^{-3}\right)^{4}}{\left(30\times 10^{-3}\right)^{2}\pi }}}$$

Cancel out \pi in both numerator and denominator.

$$\frac{2\sqrt{2}}{\sqrt{\frac{\frac{1}{64}\times \left(60\times 10^{-3}\right)^{4}}{\left(30\times 10^{-3}\right)^{2}}}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{2\sqrt{2}}{\sqrt{\frac{\frac{1}{64}\times \left(60\times \frac{1}{1000}\right)^{4}}{\left(30\times 10^{-3}\right)^{2}}}}$$

Multiply 60 and \frac{1}{1000} to get \frac{3}{50}.

$$\frac{2\sqrt{2}}{\sqrt{\frac{\frac{1}{64}\times \left(\frac{3}{50}\right)^{4}}{\left(30\times 10^{-3}\right)^{2}}}}$$

Calculate \frac{3}{50} to the power of 4 and get \frac{81}{6250000}.

$$\frac{2\sqrt{2}}{\sqrt{\frac{\frac{1}{64}\times \frac{81}{6250000}}{\left(30\times 10^{-3}\right)^{2}}}}$$

Multiply \frac{1}{64} and \frac{81}{6250000} to get \frac{81}{400000000}.

$$\frac{2\sqrt{2}}{\sqrt{\frac{\frac{81}{400000000}}{\left(30\times 10^{-3}\right)^{2}}}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{2\sqrt{2}}{\sqrt{\frac{\frac{81}{400000000}}{\left(30\times \frac{1}{1000}\right)^{2}}}}$$

Multiply 30 and \frac{1}{1000} to get \frac{3}{100}.

$$\frac{2\sqrt{2}}{\sqrt{\frac{\frac{81}{400000000}}{\left(\frac{3}{100}\right)^{2}}}}$$

Calculate \frac{3}{100} to the power of 2 and get \frac{9}{10000}.

$$\frac{2\sqrt{2}}{\sqrt{\frac{\frac{81}{400000000}}{\frac{9}{10000}}}}$$

Divide \frac{81}{400000000} by \frac{9}{10000} by multiplying \frac{81}{400000000} by the reciprocal of \frac{9}{10000}.

$$\frac{2\sqrt{2}}{\sqrt{\frac{81}{400000000}\times \frac{10000}{9}}}$$

Multiply \frac{81}{400000000} and \frac{10000}{9} to get \frac{9}{40000}.

$$\frac{2\sqrt{2}}{\sqrt{\frac{9}{40000}}}$$

Rewrite the square root of the division \frac{9}{40000} as the division of square roots \frac{\sqrt{9}}{\sqrt{40000}}. Take the square root of both numerator and denominator.

$$\frac{2\sqrt{2}}{\frac{3}{200}}$$

Divide 2\sqrt{2} by \frac{3}{200} by multiplying 2\sqrt{2} by the reciprocal of \frac{3}{200}.

$$\frac{2\sqrt{2}\times 200}{3}$$

Multiply 2 and 200 to get 400.

$$\frac{400\sqrt{2}}{3}$$