Solve sqrt{1/5}*sqrt{45}

$$\sqrt{ \frac{ 1 }{ 5 } } \times \sqrt{ 45 }$$

Evaluate

$$3$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$\frac{\sqrt{1}}{\sqrt{5}}\sqrt{45}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{5}}\sqrt{45}$$

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

$$\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\sqrt{45}$$

The square of \sqrt{5} is 5.

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

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}.

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

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

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

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

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

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

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

Cancel out 5 and 5.

$$3$$

Factor

$$3$$