Solve sqrt{4+10^14/3*10^5}

$$\sqrt { \frac { 4 + 10 ^ { 14 } } { 3 * 10 ^ { 5 } } }$$

Evaluate

$$\frac{\sqrt{750000000000030}}{1500}\approx 18257.418583506$$

Solution Steps

Calculate 10 to the power of 14 and get 100000000000000.

$$\sqrt{\frac{4+100000000000000}{3\times 10^{5}}}$$

Add 4 and 100000000000000 to get 100000000000004.

$$\sqrt{\frac{100000000000004}{3\times 10^{5}}}$$

Calculate 10 to the power of 5 and get 100000.

$$\sqrt{\frac{100000000000004}{3\times 100000}}$$

Multiply 3 and 100000 to get 300000.

$$\sqrt{\frac{100000000000004}{300000}}$$

Reduce the fraction \frac{100000000000004}{300000} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{25000000000001}{75000}}$$

Rewrite the square root of the division \sqrt{\frac{25000000000001}{75000}} as the division of square roots \frac{\sqrt{25000000000001}}{\sqrt{75000}}.

$$\frac{\sqrt{25000000000001}}{\sqrt{75000}}$$

Factor 75000=50^{2}\times 30. Rewrite the square root of the product \sqrt{50^{2}\times 30} as the product of square roots \sqrt{50^{2}}\sqrt{30}. Take the square root of 50^{2}.

$$\frac{\sqrt{25000000000001}}{50\sqrt{30}}$$

Rationalize the denominator of \frac{\sqrt{25000000000001}}{50\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{\sqrt{25000000000001}\sqrt{30}}{50\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{\sqrt{25000000000001}\sqrt{30}}{50\times 30}$$

To multiply \sqrt{25000000000001} and \sqrt{30}, multiply the numbers under the square root.

$$\frac{\sqrt{750000000000030}}{50\times 30}$$

Multiply 50 and 30 to get 1500.

$$\frac{\sqrt{750000000000030}}{1500}$$