Solve frac{sqrt{34}*sqrt{250/36}}{2}

$$\frac { \sqrt { 34 } \cdot \sqrt { \frac { 250 } { 36 } } } { 2 }$$

Evaluate

$$\frac{5\sqrt{85}}{6}\approx 7.682953714$$

Solution Steps

Reduce the fraction \frac{250}{36} to lowest terms by extracting and canceling out 2.

$$\frac{\sqrt{34}\sqrt{\frac{125}{18}}}{2}$$

Rewrite the square root of the division \sqrt{\frac{125}{18}} as the division of square roots \frac{\sqrt{125}}{\sqrt{18}}.

$$\frac{\sqrt{34}\times \frac{\sqrt{125}}{\sqrt{18}}}{2}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$\frac{\sqrt{34}\times \frac{5\sqrt{5}}{\sqrt{18}}}{2}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{\sqrt{34}\times \frac{5\sqrt{5}}{3\sqrt{2}}}{2}$$

Rationalize the denominator of \frac{5\sqrt{5}}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{34}\times \frac{5\sqrt{5}\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}}{2}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{34}\times \frac{5\sqrt{5}\sqrt{2}}{3\times 2}}{2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{34}\times \frac{5\sqrt{10}}{3\times 2}}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{\sqrt{34}\times \frac{5\sqrt{10}}{6}}{2}$$

Express \sqrt{34}\times \frac{5\sqrt{10}}{6} as a single fraction.

$$\frac{\frac{\sqrt{34}\times 5\sqrt{10}}{6}}{2}$$

Express \frac{\frac{\sqrt{34}\times 5\sqrt{10}}{6}}{2} as a single fraction.

$$\frac{\sqrt{34}\times 5\sqrt{10}}{6\times 2}$$

To multiply \sqrt{34} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{340}\times 5}{6\times 2}$$

Multiply 6 and 2 to get 12.

$$\frac{\sqrt{340}\times 5}{12}$$

Factor 340=2^{2}\times 85. Rewrite the square root of the product \sqrt{2^{2}\times 85} as the product of square roots \sqrt{2^{2}}\sqrt{85}. Take the square root of 2^{2}.

$$\frac{2\sqrt{85}\times 5}{12}$$

Multiply 2 and 5 to get 10.

$$\frac{10\sqrt{85}}{12}$$

Divide 10\sqrt{85} by 12 to get \frac{5}{6}\sqrt{85}.

$$\frac{5}{6}\sqrt{85}$$