Solve 1div6.285^-9sqrt{64700^2+44700^2}

$$1 \div 6.28 { 5 }^{ -9 } \sqrt{ 6 { 4700 }^{ 2 } +4 { 4700 }^{ 2 } }$$

Evaluate

$$\frac{188\sqrt{10}}{490625}\approx 0.001211736$$

Solution Steps

Expand \frac{1}{6.28} by multiplying both numerator and the denominator by 100.

$$\frac{100}{628}\times 5^{-9}\sqrt{6\times 4700^{2}+4\times 4700^{2}}$$

Reduce the fraction \frac{100}{628} to lowest terms by extracting and canceling out 4.

$$\frac{25}{157}\times 5^{-9}\sqrt{6\times 4700^{2}+4\times 4700^{2}}$$

Calculate 5 to the power of -9 and get \frac{1}{1953125}.

$$\frac{25}{157}\times \frac{1}{1953125}\sqrt{6\times 4700^{2}+4\times 4700^{2}}$$

Multiply \frac{25}{157} and \frac{1}{1953125} to get \frac{1}{12265625}.

$$\frac{1}{12265625}\sqrt{6\times 4700^{2}+4\times 4700^{2}}$$

Calculate 4700 to the power of 2 and get 22090000.

$$\frac{1}{12265625}\sqrt{6\times 22090000+4\times 4700^{2}}$$

Multiply 6 and 22090000 to get 132540000.

$$\frac{1}{12265625}\sqrt{132540000+4\times 4700^{2}}$$

Calculate 4700 to the power of 2 and get 22090000.

$$\frac{1}{12265625}\sqrt{132540000+4\times 22090000}$$

Multiply 4 and 22090000 to get 88360000.

$$\frac{1}{12265625}\sqrt{132540000+88360000}$$

Add 132540000 and 88360000 to get 220900000.

$$\frac{1}{12265625}\sqrt{220900000}$$

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}.

$$\frac{1}{12265625}\times 4700\sqrt{10}$$

Multiply \frac{1}{12265625} and 4700 to get \frac{188}{490625}.

$$\frac{188}{490625}\sqrt{10}$$