Solve 1/27.14*sqrt{0.034/0.43*10^-6}

$$\frac{ 1 }{ 27.14 } \times \sqrt{ \frac{ 0.034 }{ 0.43 \times { 10 }^{ -6 } } }$$

Evaluate

$$\frac{10000\sqrt{3655}}{58351}\approx 10.360850028$$

Solution Steps

Expand \frac{1}{27.14} by multiplying both numerator and the denominator by 100.

$$\frac{100}{2714}\sqrt{\frac{0.034}{0.43\times 10^{-6}}}$$

Reduce the fraction \frac{100}{2714} to lowest terms by extracting and canceling out 2.

$$\frac{50}{1357}\sqrt{\frac{0.034}{0.43\times 10^{-6}}}$$

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

$$\frac{50}{1357}\sqrt{\frac{0.034}{0.43\times \frac{1}{1000000}}}$$

Multiply 0.43 and \frac{1}{1000000} to get \frac{43}{100000000}.

$$\frac{50}{1357}\sqrt{\frac{0.034}{\frac{43}{100000000}}}$$

Divide 0.034 by \frac{43}{100000000} by multiplying 0.034 by the reciprocal of \frac{43}{100000000}.

$$\frac{50}{1357}\sqrt{0.034\times \frac{100000000}{43}}$$

Multiply 0.034 and \frac{100000000}{43} to get \frac{3400000}{43}.

$$\frac{50}{1357}\sqrt{\frac{3400000}{43}}$$

Rewrite the square root of the division \sqrt{\frac{3400000}{43}} as the division of square roots \frac{\sqrt{3400000}}{\sqrt{43}}.

$$\frac{50}{1357}\times \frac{\sqrt{3400000}}{\sqrt{43}}$$

Factor 3400000=200^{2}\times 85. Rewrite the square root of the product \sqrt{200^{2}\times 85} as the product of square roots \sqrt{200^{2}}\sqrt{85}. Take the square root of 200^{2}.

$$\frac{50}{1357}\times \frac{200\sqrt{85}}{\sqrt{43}}$$

Rationalize the denominator of \frac{200\sqrt{85}}{\sqrt{43}} by multiplying numerator and denominator by \sqrt{43}.

$$\frac{50}{1357}\times \frac{200\sqrt{85}\sqrt{43}}{\left(\sqrt{43}\right)^{2}}$$

The square of \sqrt{43} is 43.

$$\frac{50}{1357}\times \frac{200\sqrt{85}\sqrt{43}}{43}$$

To multiply \sqrt{85} and \sqrt{43}, multiply the numbers under the square root.

$$\frac{50}{1357}\times \frac{200\sqrt{3655}}{43}$$

Multiply \frac{50}{1357} times \frac{200\sqrt{3655}}{43} by multiplying numerator times numerator and denominator times denominator.

$$\frac{50\times 200\sqrt{3655}}{1357\times 43}$$

Multiply 50 and 200 to get 10000.

$$\frac{10000\sqrt{3655}}{1357\times 43}$$

Multiply 1357 and 43 to get 58351.

$$\frac{10000\sqrt{3655}}{58351}$$