Solve sqrt{500+400/3}=

$$\sqrt { 500 + \frac { 400 } { 3 } } =$$

Evaluate

$$\frac{10\sqrt{57}}{3}\approx 25.166114784$$

Solution Steps

Convert 500 to fraction \frac{1500}{3}.

$$\sqrt{\frac{1500}{3}+\frac{400}{3}}$$

Since \frac{1500}{3} and \frac{400}{3} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{1500+400}{3}}$$

Add 1500 and 400 to get 1900.

$$\sqrt{\frac{1900}{3}}$$

Rewrite the square root of the division \sqrt{\frac{1900}{3}} as the division of square roots \frac{\sqrt{1900}}{\sqrt{3}}.

$$\frac{\sqrt{1900}}{\sqrt{3}}$$

Factor 1900=10^{2}\times 19. Rewrite the square root of the product \sqrt{10^{2}\times 19} as the product of square roots \sqrt{10^{2}}\sqrt{19}. Take the square root of 10^{2}.

$$\frac{10\sqrt{19}}{\sqrt{3}}$$

Rationalize the denominator of \frac{10\sqrt{19}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{10\sqrt{19}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{10\sqrt{19}\sqrt{3}}{3}$$

To multiply \sqrt{19} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{10\sqrt{57}}{3}$$