Solve 5sqrt{5/8}*1sqrt{5/9}

$$5 \sqrt{ \frac{ 5 }{ 8 } } \times 1 \sqrt{ \frac{ 5 }{ 9 } }$$

Evaluate

$$\frac{25\sqrt{2}}{12}\approx 2.946278255$$

Solution Steps

To multiply \sqrt{\frac{5}{8}} and \sqrt{\frac{5}{9}}, multiply the numbers under the square root.

$$1\times 5\sqrt{\frac{25}{72}}$$

Multiply 1 and 5 to get 5.

$$5\sqrt{\frac{25}{72}}$$

Rewrite the square root of the division \sqrt{\frac{25}{72}} as the division of square roots \frac{\sqrt{25}}{\sqrt{72}}.

$$5\times \frac{\sqrt{25}}{\sqrt{72}}$$

Calculate the square root of 25 and get 5.

$$5\times \frac{5}{\sqrt{72}}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

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

Rationalize the denominator of \frac{5}{6\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$5\times \frac{5\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

Multiply 6 and 2 to get 12.

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

Express 5\times \frac{5\sqrt{2}}{12} as a single fraction.

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

Multiply 5 and 5 to get 25.

$$\frac{25\sqrt{2}}{12}$$