Solve sqrt{52}*sqrt{13/9}

$$\sqrt { 52 } \times \sqrt { \frac { 13 } { 9 } }$$

Evaluate

$$\frac{26}{3}\approx 8.666666667$$

Solution Steps

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$2\sqrt{13}\sqrt{\frac{13}{9}}$$

Rewrite the square root of the division \sqrt{\frac{13}{9}} as the division of square roots \frac{\sqrt{13}}{\sqrt{9}}.

$$2\sqrt{13}\times \frac{\sqrt{13}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$2\sqrt{13}\times \frac{\sqrt{13}}{3}$$

Express 2\times \frac{\sqrt{13}}{3} as a single fraction.

$$\frac{2\sqrt{13}}{3}\sqrt{13}$$

Express \frac{2\sqrt{13}}{3}\sqrt{13} as a single fraction.

$$\frac{2\sqrt{13}\sqrt{13}}{3}$$

Multiply \sqrt{13} and \sqrt{13} to get 13.

$$\frac{2\times 13}{3}$$

Multiply 2 and 13 to get 26.

$$\frac{26}{3}$$

Factor

$$\frac{2 \cdot 13}{3} = 8\frac{2}{3} = 8.666666666666666$$