Solve sqrt{64*6/94^5}=

$$\sqrt { \frac { 64 \times 6 } { 94 ^ { 5 } } } =$$

Evaluate

$$\frac{2\sqrt{141}}{103823}\approx 0.000228742$$

Solution Steps

Multiply 64 and 6 to get 384.

$$\sqrt{\frac{384}{94^{5}}}$$

Calculate 94 to the power of 5 and get 7339040224.

$$\sqrt{\frac{384}{7339040224}}$$

Reduce the fraction \frac{384}{7339040224} to lowest terms by extracting and canceling out 32.

$$\sqrt{\frac{12}{229345007}}$$

Rewrite the square root of the division \sqrt{\frac{12}{229345007}} as the division of square roots \frac{\sqrt{12}}{\sqrt{229345007}}.

$$\frac{\sqrt{12}}{\sqrt{229345007}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{2\sqrt{3}}{\sqrt{229345007}}$$

Factor 229345007=2209^{2}\times 47. Rewrite the square root of the product \sqrt{2209^{2}\times 47} as the product of square roots \sqrt{2209^{2}}\sqrt{47}. Take the square root of 2209^{2}.

$$\frac{2\sqrt{3}}{2209\sqrt{47}}$$

Rationalize the denominator of \frac{2\sqrt{3}}{2209\sqrt{47}} by multiplying numerator and denominator by \sqrt{47}.

$$\frac{2\sqrt{3}\sqrt{47}}{2209\left(\sqrt{47}\right)^{2}}$$

The square of \sqrt{47} is 47.

$$\frac{2\sqrt{3}\sqrt{47}}{2209\times 47}$$

To multiply \sqrt{3} and \sqrt{47}, multiply the numbers under the square root.

$$\frac{2\sqrt{141}}{2209\times 47}$$

Multiply 2209 and 47 to get 103823.

$$\frac{2\sqrt{141}}{103823}$$