Solve frac{sqrt{15}sqrt{5}}{sqrt{3}}

$$\frac{ \sqrt{ 15 } \sqrt{ 5 } }{ \sqrt{ 3 } }$$

Evaluate

$$5$$

Solution Steps

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

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

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

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

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

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

The square of \sqrt{3} is 3.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Multiply 5 and 3 to get 15.

$$\frac{15}{3}$$

Divide 15 by 3 to get 5.

$$5$$

Factor

$$5$$