Solve sqrt{(10^6)^2/3}

$$\sqrt { \frac { ( 10 ^ { 6 } ) ^ { 2 } } { 3 } }$$

Evaluate

$$\frac{1000000\sqrt{3}}{3}\approx 577350.269189626$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\sqrt{\frac{10^{12}}{3}}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\sqrt{\frac{1000000000000}{3}}$$

Rewrite the square root of the division \sqrt{\frac{1000000000000}{3}} as the division of square roots \frac{\sqrt{1000000000000}}{\sqrt{3}}.

$$\frac{\sqrt{1000000000000}}{\sqrt{3}}$$

Calculate the square root of 1000000000000 and get 1000000.

$$\frac{1000000}{\sqrt{3}}$$

Rationalize the denominator of \frac{1000000}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{1000000\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{1000000\sqrt{3}}{3}$$