Solve frac{2sqrt{18}}{sqrt{24}}

$$\frac { 2 \sqrt { 18 } } { \sqrt { 24 } }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{2\times 3\sqrt{2}}{\sqrt{24}}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{2}}{\sqrt{24}}$$

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}.

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

Cancel out 2 in both numerator and denominator.

$$\frac{3\sqrt{2}}{\sqrt{6}}$$

Rationalize the denominator of \frac{3\sqrt{2}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

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

The square of \sqrt{6} is 6.

$$\frac{3\sqrt{2}\sqrt{6}}{6}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$\frac{3\sqrt{2}\sqrt{2}\sqrt{3}}{6}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{3\times 2\sqrt{3}}{6}$$

Multiply 3 and 2 to get 6.

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

Cancel out 6 and 6.

$$\sqrt{3}$$