Solve sqrt{13-25/9}

$$\sqrt { 13 - \frac { 25 } { 9 } }$$

Evaluate

$$\frac{2\sqrt{23}}{3}\approx 3.197221016$$

Solution Steps

Convert 13 to fraction \frac{117}{9}.

$$\sqrt{\frac{117}{9}-\frac{25}{9}}$$

Since \frac{117}{9} and \frac{25}{9} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{117-25}{9}}$$

Subtract 25 from 117 to get 92.

$$\sqrt{\frac{92}{9}}$$

Rewrite the square root of the division \sqrt{\frac{92}{9}} as the division of square roots \frac{\sqrt{92}}{\sqrt{9}}.

$$\frac{\sqrt{92}}{\sqrt{9}}$$

Factor 92=2^{2}\times 23. Rewrite the square root of the product \sqrt{2^{2}\times 23} as the product of square roots \sqrt{2^{2}}\sqrt{23}. Take the square root of 2^{2}.

$$\frac{2\sqrt{23}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{2\sqrt{23}}{3}$$