Solve frac{5sqrt{15}}{3sqrt{12}}

$$\frac { 5 \sqrt { 15 } } { 3 \sqrt { 12 } }$$

Evaluate

$$\frac{5\sqrt{5}}{6}\approx 1.863389981$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{5\sqrt{15}}{3\times 2\sqrt{3}}$$

Multiply 3 and 2 to get 6.

$$\frac{5\sqrt{15}}{6\sqrt{3}}$$

Rationalize the denominator of \frac{5\sqrt{15}}{6\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{5\sqrt{15}\sqrt{3}}{6\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{5\sqrt{15}\sqrt{3}}{6\times 3}$$

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}.

$$\frac{5\sqrt{3}\sqrt{5}\sqrt{3}}{6\times 3}$$

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

$$\frac{5\times 3\sqrt{5}}{6\times 3}$$

Multiply 6 and 3 to get 18.

$$\frac{5\times 3\sqrt{5}}{18}$$

Multiply 5 and 3 to get 15.

$$\frac{15\sqrt{5}}{18}$$

Divide 15\sqrt{5} by 18 to get \frac{5}{6}\sqrt{5}.

$$\frac{5}{6}\sqrt{5}$$