Solve 628*5^(-9)sqrt{6*4700^2+4*4700^2}

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

Evaluate

$$\frac{118064\sqrt{10}}{78125}\approx 4.778894716$$

Solution Steps

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

$$628\times \frac{1}{1953125}\sqrt{6\times 4700^{2}+4\times 4700^{2}}$$

Multiply 628 and \frac{1}{1953125} to get \frac{628}{1953125}.

$$\frac{628}{1953125}\sqrt{6\times 4700^{2}+4\times 4700^{2}}$$

Calculate 4700 to the power of 2 and get 22090000.

$$\frac{628}{1953125}\sqrt{6\times 22090000+4\times 4700^{2}}$$

Multiply 6 and 22090000 to get 132540000.

$$\frac{628}{1953125}\sqrt{132540000+4\times 4700^{2}}$$

Calculate 4700 to the power of 2 and get 22090000.

$$\frac{628}{1953125}\sqrt{132540000+4\times 22090000}$$

Multiply 4 and 22090000 to get 88360000.

$$\frac{628}{1953125}\sqrt{132540000+88360000}$$

Add 132540000 and 88360000 to get 220900000.

$$\frac{628}{1953125}\sqrt{220900000}$$

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}.

$$\frac{628}{1953125}\times 4700\sqrt{10}$$

Multiply \frac{628}{1953125} and 4700 to get \frac{118064}{78125}.

$$\frac{118064}{78125}\sqrt{10}$$