Solve sqrt{50}-sqrt{18}+sqrt{32}*(a)*sqrt{1}

$$\sqrt { 50 } - \sqrt { 18 } + \sqrt { 32 } \cdot ( a ) \cdot \sqrt { 1 }$$

Evaluate

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

Solution Steps

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}.

$$5\sqrt{2}-\sqrt{18}+\sqrt{32}a\sqrt{1}$$

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}.

$$5\sqrt{2}-3\sqrt{2}+\sqrt{32}a\sqrt{1}$$

Combine 5\sqrt{2} and -3\sqrt{2} to get 2\sqrt{2}.

$$2\sqrt{2}+\sqrt{32}a\sqrt{1}$$

Factor 32=1\times 32. Rewrite the square root of the product \sqrt{1\times 32} as the product of square roots \sqrt{1}\sqrt{32}.

$$2\sqrt{2}+\sqrt{1}\sqrt{32}a\sqrt{1}$$

Multiply \sqrt{1} and \sqrt{1} to get 1.

$$2\sqrt{2}+1a\sqrt{32}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$2\sqrt{2}+1a\times 4\sqrt{2}$$

Multiply 1 and 4 to get 4.

$$2\sqrt{2}+4a\sqrt{2}$$

Differentiate w.r.t. a

$$4 \sqrt{2} = 5.656854249$$