Solve 1/2a*(sqrt{8}+sqrt{32})*sqrt{3}=300

$$\frac { 1 } { 2 } a \cdot ( \sqrt { 8 } + \sqrt { 32 } ) \cdot \sqrt { 3 } = 300$$

Solve for a

$$a = \frac{50 \sqrt{6}}{3} \approx 40.824829046$$

Steps for Solving Linear Equation

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}.

$$\frac{1}{2}a\left(2\sqrt{2}+\sqrt{32}\right)\sqrt{3}=300$$

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}.

$$\frac{1}{2}a\left(2\sqrt{2}+4\sqrt{2}\right)\sqrt{3}=300$$

Combine 2\sqrt{2} and 4\sqrt{2} to get 6\sqrt{2}.

$$\frac{1}{2}a\times 6\sqrt{2}\sqrt{3}=300$$

Multiply \frac{1}{2} and 6 to get \frac{6}{2}.

$$\frac{6}{2}a\sqrt{2}\sqrt{3}=300$$

Divide 6 by 2 to get 3.

$$3a\sqrt{2}\sqrt{3}=300$$

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

$$3a\sqrt{6}=300$$

The equation is in standard form.

$$3\sqrt{6}a=300$$

Divide both sides by 3\sqrt{6}.

$$\frac{3\sqrt{6}a}{3\sqrt{6}}=\frac{300}{3\sqrt{6}}$$

Dividing by 3\sqrt{6} undoes the multiplication by 3\sqrt{6}.

$$a=\frac{300}{3\sqrt{6}}$$

Divide 300 by 3\sqrt{6}.

$$a=\frac{50\sqrt{6}}{3}$$