Solve 2sqrt{18}*sqrt{48}:sqrt{72}

$$2 \sqrt { 18 } \times \sqrt { 48 } : \sqrt { 72 }$$

Evaluate

$$4\sqrt{3}\approx 6.92820323$$

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}.

$$\frac{2\times 3\sqrt{2}\sqrt{48}}{\sqrt{72}}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{2}\sqrt{48}}{\sqrt{72}}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{6\sqrt{2}\times 4\sqrt{3}}{\sqrt{72}}$$

Multiply 6 and 4 to get 24.

$$\frac{24\sqrt{2}\sqrt{3}}{\sqrt{72}}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{24\sqrt{6}}{\sqrt{72}}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

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

Cancel out 6 in both numerator and denominator.

$$\frac{4\sqrt{6}}{\sqrt{2}}$$

Rationalize the denominator of \frac{4\sqrt{6}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4\sqrt{6}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{4\sqrt{6}\sqrt{2}}{2}$$

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}.

$$\frac{4\sqrt{2}\sqrt{3}\sqrt{2}}{2}$$

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

$$\frac{4\times 2\sqrt{3}}{2}$$

Cancel out 2 and 2.

$$4\sqrt{3}$$