Solve 2sqrt{8}-3sqrt{18}+5sqrt{12}

$$2 \sqrt { 8 } - 3 \sqrt { 18 } + 5 \sqrt { 12 }$$

Evaluate

$$5\sqrt{2}\left(\sqrt{6}-1\right)\approx 10.249440264$$

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}.

$$2\times 2\sqrt{2}-3\sqrt{18}+5\sqrt{12}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{2}-3\sqrt{18}+5\sqrt{12}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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

Multiply -3 and 3 to get -9.

$$4\sqrt{2}-9\sqrt{2}+5\sqrt{12}$$

Combine 4\sqrt{2} and -9\sqrt{2} to get -5\sqrt{2}.

$$-5\sqrt{2}+5\sqrt{12}$$

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}.

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

Multiply 5 and 2 to get 10.

$$-5\sqrt{2}+10\sqrt{3}$$