Solve 35/22*16/8sqrt{45}

$$\frac{ 35 }{ 22 } \times \frac{ 16 }{ 8 \sqrt{ 45 } }$$

Evaluate

$$\frac{7\sqrt{5}}{33}\approx 0.47431745$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{35}{22}\times \frac{16}{8\times 3\sqrt{5}}$$

Multiply 8 and 3 to get 24.

$$\frac{35}{22}\times \frac{16}{24\sqrt{5}}$$

Rationalize the denominator of \frac{16}{24\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{35}{22}\times \frac{16\sqrt{5}}{24\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{35}{22}\times \frac{16\sqrt{5}}{24\times 5}$$

Cancel out 8 in both numerator and denominator.

$$\frac{35}{22}\times \frac{2\sqrt{5}}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{35}{22}\times \frac{2\sqrt{5}}{15}$$

Multiply \frac{35}{22} times \frac{2\sqrt{5}}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 2\sqrt{5}}{22\times 15}$$

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{7\sqrt{5}}{3\times 11}$$

Multiply 3 and 11 to get 33.

$$\frac{7\sqrt{5}}{33}$$