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

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

Evaluate

$$4\sqrt{6}\left(\sqrt{15}-2\right)\approx 18.35141398$$

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}.

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

Multiply 2 and 2 to get 4.

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

Use the distributive property to multiply 4\sqrt{2} by 3\sqrt{5}-2\sqrt{3}.

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

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

$$12\sqrt{10}-8\sqrt{3}\sqrt{2}$$

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

$$12\sqrt{10}-8\sqrt{6}$$

Factor

$$4 \sqrt{6} {(\sqrt{15} - 2)} = 18.35141398$$