Solve quad2sqrt{8}+sqrt{12}-sqrt{50}

$$\quad 2 \sqrt { 8 } + \sqrt { 12 } - \sqrt { 50 }$$

Evaluate

$$\sqrt{2}\left(\sqrt{6}-1\right)\approx 2.049888053$$

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}.

$$2\times 2\sqrt{2}+\sqrt{12}-\sqrt{50}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{2}+\sqrt{12}-\sqrt{50}$$

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}.

$$4\sqrt{2}+2\sqrt{3}-\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

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

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

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