Solve 700^4/sqrt{21*19^2}

$$\frac { 700 ^ { 4 } } { \sqrt { 21 \times 19 ^ { 2 } } }$$

Evaluate

$$\frac{34300000000\sqrt{21}}{57}\approx 2757585023.455883026$$

Solution Steps

Calculate 700 to the power of 4 and get 240100000000.

$$\frac{240100000000}{\sqrt{21\times 19^{2}}}$$

Calculate 19 to the power of 2 and get 361.

$$\frac{240100000000}{\sqrt{21\times 361}}$$

Multiply 21 and 361 to get 7581.

$$\frac{240100000000}{\sqrt{7581}}$$

Factor 7581=19^{2}\times 21. Rewrite the square root of the product \sqrt{19^{2}\times 21} as the product of square roots \sqrt{19^{2}}\sqrt{21}. Take the square root of 19^{2}.

$$\frac{240100000000}{19\sqrt{21}}$$

Rationalize the denominator of \frac{240100000000}{19\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$\frac{240100000000\sqrt{21}}{19\left(\sqrt{21}\right)^{2}}$$

The square of \sqrt{21} is 21.

$$\frac{240100000000\sqrt{21}}{19\times 21}$$

Cancel out 7 in both numerator and denominator.

$$\frac{34300000000\sqrt{21}}{3\times 19}$$

Multiply 3 and 19 to get 57.

$$\frac{34300000000\sqrt{21}}{57}$$