Solve frac{sqrt{15}}{3}divfrac{sqrt{30}}{6}

$$\frac { \sqrt { 15 } } { 3 } \div \frac { \sqrt { 30 } } { 6 }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Divide \frac{\sqrt{15}}{3} by \frac{\sqrt{30}}{6} by multiplying \frac{\sqrt{15}}{3} by the reciprocal of \frac{\sqrt{30}}{6}.

$$\frac{\sqrt{15}\times 6}{3\sqrt{30}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\sqrt{15}}{\sqrt{30}}$$

Rationalize the denominator of \frac{2\sqrt{15}}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{2\sqrt{15}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{2\sqrt{15}\sqrt{30}}{30}$$

Factor 30=15\times 2. Rewrite the square root of the product \sqrt{15\times 2} as the product of square roots \sqrt{15}\sqrt{2}.

$$\frac{2\sqrt{15}\sqrt{15}\sqrt{2}}{30}$$

Multiply \sqrt{15} and \sqrt{15} to get 15.

$$\frac{2\times 15\sqrt{2}}{30}$$

Multiply 2 and 15 to get 30.

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

Cancel out 30 and 30.

$$\sqrt{2}$$