Solve 2sqrt{2}(3sqrt{12}-8sqrt{5})

$$2 \sqrt { 2 } ( 3 \sqrt { 12 } - 8 \sqrt { 5 } )$$

Evaluate

$$4\sqrt{2}\left(3\sqrt{3}-4\sqrt{5}\right)\approx -21.202565649$$

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}.

$$2\sqrt{2}\left(3\times 2\sqrt{3}-8\sqrt{5}\right)$$

Multiply 3 and 2 to get 6.

$$2\sqrt{2}\left(6\sqrt{3}-8\sqrt{5}\right)$$

Use the distributive property to multiply 2\sqrt{2} by 6\sqrt{3}-8\sqrt{5}.

$$12\sqrt{3}\sqrt{2}-16\sqrt{2}\sqrt{5}$$

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

$$12\sqrt{6}-16\sqrt{2}\sqrt{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$12\sqrt{6}-16\sqrt{10}$$