Solve sqrt{24}divsqrt{30}

$$\sqrt { 24 } \div \sqrt { 30 }$$

Evaluate

$$\frac{2\sqrt{5}}{5}\approx 0.894427191$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{2\sqrt{6}}{\sqrt{30}}$$

Rationalize the denominator of \frac{2\sqrt{6}}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{2\sqrt{6}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{2\sqrt{6}\sqrt{30}}{30}$$

Factor 30=6\times 5. Rewrite the square root of the product \sqrt{6\times 5} as the product of square roots \sqrt{6}\sqrt{5}.

$$\frac{2\sqrt{6}\sqrt{6}\sqrt{5}}{30}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{2\times 6\sqrt{5}}{30}$$

Multiply 2 and 6 to get 12.

$$\frac{12\sqrt{5}}{30}$$

Divide 12\sqrt{5} by 30 to get \frac{2}{5}\sqrt{5}.

$$\frac{2}{5}\sqrt{5}$$