Solve 16div5/sqrt{45}

$$\frac { 16 \div 5 } { \sqrt { 45 } }$$

Evaluate

$$\frac{16\sqrt{5}}{75}\approx 0.477027835$$

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}.

$$\frac{\frac{16}{5}}{3\sqrt{5}}$$

Express \frac{\frac{16}{5}}{3\sqrt{5}} as a single fraction.

$$\frac{16}{5\times 3\sqrt{5}}$$

Rationalize the denominator of \frac{16}{5\times 3\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{16\sqrt{5}}{5\times 3\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{16\sqrt{5}}{5\times 3\times 5}$$

Multiply 5 and 3 to get 15.

$$\frac{16\sqrt{5}}{15\times 5}$$

Multiply 15 and 5 to get 75.

$$\frac{16\sqrt{5}}{75}$$