Solve 2sqrt{6}*sqrt{8}

$$2 \sqrt { 6 } \times \sqrt { 8 }$$

Evaluate

$$8\sqrt{3}\approx 13.856406461$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Multiply 2 and 2 to get 4.

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

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}.

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

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

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

Multiply 4 and 2 to get 8.

$$8\sqrt{3}$$