Solve sqrt{30*(1000/9)}

$$\sqrt { 30 \times ( \frac { 1000 } { 9 } ) }$$

Evaluate

$$\frac{100\sqrt{3}}{3}\approx 57.735026919$$

Solution Steps

Express 30\times \frac{1000}{9} as a single fraction.

$$\sqrt{\frac{30\times 1000}{9}}$$

Multiply 30 and 1000 to get 30000.

$$\sqrt{\frac{30000}{9}}$$

Reduce the fraction \frac{30000}{9} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{10000}{3}}$$

Rewrite the square root of the division \sqrt{\frac{10000}{3}} as the division of square roots \frac{\sqrt{10000}}{\sqrt{3}}.

$$\frac{\sqrt{10000}}{\sqrt{3}}$$

Calculate the square root of 10000 and get 100.

$$\frac{100}{\sqrt{3}}$$

Rationalize the denominator of \frac{100}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{100\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{100\sqrt{3}}{3}$$