Solve 2sqrt{3}*sqrt{8}-5sqrt{2}*sqrt{12}

$$2 \sqrt { 3 } \cdot \sqrt { 8 } - 5 \sqrt { 2 } \cdot \sqrt { 12 }$$

Evaluate

$$-6\sqrt{6}\approx -14.696938457$$

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}.

$$2\sqrt{3}\times 2\sqrt{2}-5\sqrt{2}\sqrt{12}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{3}\sqrt{2}-5\sqrt{2}\sqrt{12}$$

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

$$4\sqrt{6}-5\sqrt{2}\sqrt{12}$$

Factor 12=2\times 6. Rewrite the square root of the product \sqrt{2\times 6} as the product of square roots \sqrt{2}\sqrt{6}.

$$4\sqrt{6}-5\sqrt{2}\sqrt{2}\sqrt{6}$$

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

$$4\sqrt{6}-5\times 2\sqrt{6}$$

Multiply 5 and 2 to get 10.

$$4\sqrt{6}-10\sqrt{6}$$

Combine 4\sqrt{6} and -10\sqrt{6} to get -6\sqrt{6}.

$$-6\sqrt{6}$$