Solve sqrt{6}sqrt{32}=

$$\sqrt { 6 } \sqrt { 32 } =$$

Evaluate

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

Solution Steps

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}.

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

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}.

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

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

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

Multiply 2 and 4 to get 8.

$$8\sqrt{3}$$