Solve 2sqrt{18}-sqrt{50}+sqrt{72}a

$$2 \sqrt { 18 } - \sqrt { 50 } + \sqrt { 72 } a$$

Evaluate

$$\sqrt{2}\left(6a+1\right)$$

Solution Steps

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}.

$$2\times 3\sqrt{2}-\sqrt{50}+\sqrt{72}a$$

Multiply 2 and 3 to get 6.

$$6\sqrt{2}-\sqrt{50}+\sqrt{72}a$$

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}.

$$6\sqrt{2}-5\sqrt{2}+\sqrt{72}a$$

Combine 6\sqrt{2} and -5\sqrt{2} to get \sqrt{2}.

$$\sqrt{2}+\sqrt{72}a$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\sqrt{2}+6\sqrt{2}a$$

Differentiate w.r.t. a

$$6 \sqrt{2} = 8.485281374$$