Solve frac{6sqrt{3}*8sqrt{2}}{sqrt{32}*sqrt{27}}

$$\frac { 6 \sqrt { 3 } \times 8 \sqrt { 2 } } { \sqrt { 32 } \times \sqrt { 27 } }$$

Evaluate

$$4$$

Solution Steps

Multiply 6 and 8 to get 48.

$$\frac{48\sqrt{3}\sqrt{2}}{\sqrt{32}\sqrt{27}}$$

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

$$\frac{48\sqrt{6}}{\sqrt{32}\sqrt{27}}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{48\sqrt{6}}{4\sqrt{2}\sqrt{27}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{48\sqrt{6}}{4\sqrt{2}\times 3\sqrt{3}}$$

Multiply 4 and 3 to get 12.

$$\frac{48\sqrt{6}}{12\sqrt{2}\sqrt{3}}$$

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

$$\frac{48\sqrt{6}}{12\sqrt{6}}$$

Cancel out 12\sqrt{6} in both numerator and denominator.

$$4$$

Factor

$$2^{2}$$