Solve sqrt{15}divsqrt{27}

$$\sqrt{ 15 } \div \sqrt{ 27 }$$

Evaluate

$$\frac{\sqrt{5}}{3}\approx 0.745355992$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Rationalize the denominator of \frac{\sqrt{15}}{3\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{15}\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

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

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

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

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

Multiply 3 and 3 to get 9.

$$\frac{3\sqrt{5}}{9}$$

Divide 3\sqrt{5} by 9 to get \frac{1}{3}\sqrt{5}.

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