Solve 1/6.28*5^(-15)sqrt{6*4700^2+4*4700^2}

$$\frac { 1 } { 6.28 \times 5 ^ { ( - 15 ) } } \sqrt { 6 \times 4700 ^ { 2 } + 4 \times 4700 ^ { 2 } }$$

Evaluate

$$\frac{3585815429687500\sqrt{10}}{157}\approx 7.222512119 \cdot 10^{13}$$

Solution Steps

Calculate 5 to the power of -15 and get \frac{1}{30517578125}.

$$\frac{1}{6.28\times \frac{1}{30517578125}}\sqrt{6\times 4700^{2}+4\times 4700^{2}}$$

Multiply 6.28 and \frac{1}{30517578125} to get \frac{157}{762939453125}.

$$\frac{1}{\frac{157}{762939453125}}\sqrt{6\times 4700^{2}+4\times 4700^{2}}$$

Divide 1 by \frac{157}{762939453125} by multiplying 1 by the reciprocal of \frac{157}{762939453125}.

$$1\times \frac{762939453125}{157}\sqrt{6\times 4700^{2}+4\times 4700^{2}}$$

Multiply 1 and \frac{762939453125}{157} to get \frac{762939453125}{157}.

$$\frac{762939453125}{157}\sqrt{6\times 4700^{2}+4\times 4700^{2}}$$

Calculate 4700 to the power of 2 and get 22090000.

$$\frac{762939453125}{157}\sqrt{6\times 22090000+4\times 4700^{2}}$$

Multiply 6 and 22090000 to get 132540000.

$$\frac{762939453125}{157}\sqrt{132540000+4\times 4700^{2}}$$

Calculate 4700 to the power of 2 and get 22090000.

$$\frac{762939453125}{157}\sqrt{132540000+4\times 22090000}$$

Multiply 4 and 22090000 to get 88360000.

$$\frac{762939453125}{157}\sqrt{132540000+88360000}$$

Add 132540000 and 88360000 to get 220900000.

$$\frac{762939453125}{157}\sqrt{220900000}$$

Factor 220900000=4700^{2}\times 10. Rewrite the square root of the product \sqrt{4700^{2}\times 10} as the product of square roots \sqrt{4700^{2}}\sqrt{10}. Take the square root of 4700^{2}.

$$\frac{762939453125}{157}\times 4700\sqrt{10}$$

Multiply \frac{762939453125}{157} and 4700 to get \frac{3585815429687500}{157}.

$$\frac{3585815429687500}{157}\sqrt{10}$$