Solve 15divsqrt{5}*1/sqrt{5}

$$15 \div \sqrt{ 5 } \times \frac{ 1 }{ \sqrt{ 5 } }$$

Evaluate

$$3$$

Solution Steps

Rationalize the denominator of \frac{15}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{15\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times \frac{1}{\sqrt{5}}$$

The square of \sqrt{5} is 5.

$$\frac{15\sqrt{5}}{5}\times \frac{1}{\sqrt{5}}$$

Divide 15\sqrt{5} by 5 to get 3\sqrt{5}.

$$3\sqrt{5}\times \frac{1}{\sqrt{5}}$$

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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

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

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

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

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Cancel out 5 and 5.

$$3$$

Factor

$$3$$