Solve sqrt{12}*4sqrt{32}

$$\sqrt { 12 } \times 4 \sqrt { 32 }$$

Evaluate

$$32\sqrt{6}\approx 78.383671769$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$4\times 2\sqrt{3}\sqrt{32}$$

Multiply 4 and 2 to get 8.

$$8\sqrt{3}\sqrt{32}$$

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}.

$$8\sqrt{3}\times 4\sqrt{2}$$

Multiply 8 and 4 to get 32.

$$32\sqrt{3}\sqrt{2}$$

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

$$32\sqrt{6}$$