Solve 1/47.14sqrt{0.039/0.43*10^-6}

$$\frac{ 1 }{ 47.14 } \sqrt{ \frac{ 0.039 }{ 0.43 \times { 10 }^{ -6 } } }$$

Evaluate

$$\frac{5000\sqrt{16770}}{101351}\approx 6.388641195$$

Solution Steps

Expand \frac{1}{47.14} by multiplying both numerator and the denominator by 100.

$$\frac{100}{4714}\sqrt{\frac{0.039}{0.43\times 10^{-6}}}$$

Reduce the fraction \frac{100}{4714} to lowest terms by extracting and canceling out 2.

$$\frac{50}{2357}\sqrt{\frac{0.039}{0.43\times 10^{-6}}}$$

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

$$\frac{50}{2357}\sqrt{\frac{0.039}{0.43\times \frac{1}{1000000}}}$$

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

$$\frac{50}{2357}\sqrt{\frac{0.039}{\frac{43}{100000000}}}$$

Divide 0.039 by \frac{43}{100000000} by multiplying 0.039 by the reciprocal of \frac{43}{100000000}.

$$\frac{50}{2357}\sqrt{0.039\times \frac{100000000}{43}}$$

Multiply 0.039 and \frac{100000000}{43} to get \frac{3900000}{43}.

$$\frac{50}{2357}\sqrt{\frac{3900000}{43}}$$

Rewrite the square root of the division \sqrt{\frac{3900000}{43}} as the division of square roots \frac{\sqrt{3900000}}{\sqrt{43}}.

$$\frac{50}{2357}\times \frac{\sqrt{3900000}}{\sqrt{43}}$$

Factor 3900000=100^{2}\times 390. Rewrite the square root of the product \sqrt{100^{2}\times 390} as the product of square roots \sqrt{100^{2}}\sqrt{390}. Take the square root of 100^{2}.

$$\frac{50}{2357}\times \frac{100\sqrt{390}}{\sqrt{43}}$$

Rationalize the denominator of \frac{100\sqrt{390}}{\sqrt{43}} by multiplying numerator and denominator by \sqrt{43}.

$$\frac{50}{2357}\times \frac{100\sqrt{390}\sqrt{43}}{\left(\sqrt{43}\right)^{2}}$$

The square of \sqrt{43} is 43.

$$\frac{50}{2357}\times \frac{100\sqrt{390}\sqrt{43}}{43}$$

To multiply \sqrt{390} and \sqrt{43}, multiply the numbers under the square root.

$$\frac{50}{2357}\times \frac{100\sqrt{16770}}{43}$$

Multiply \frac{50}{2357} times \frac{100\sqrt{16770}}{43} by multiplying numerator times numerator and denominator times denominator.

$$\frac{50\times 100\sqrt{16770}}{2357\times 43}$$

Multiply 50 and 100 to get 5000.

$$\frac{5000\sqrt{16770}}{2357\times 43}$$

Multiply 2357 and 43 to get 101351.

$$\frac{5000\sqrt{16770}}{101351}$$