Solve {l}{a=11sqrt{8}*11sqrt{3^2}*11sqrt{12^4}}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { a = 11 \sqrt{8} \cdot 11 \sqrt{3 ^ {2}} \cdot 11 \sqrt{12 ^ {4}} }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solve for a, b, c

$$c=1149984\sqrt{2}\approx 1626322.969312062$$

Solution Steps

Consider the first equation. Multiply 11 and 11 to get 121.

$$a=121\times 11\sqrt{8}\sqrt{3^{2}}\sqrt{12^{4}}$$

Multiply 121 and 11 to get 1331.

$$a=1331\sqrt{8}\sqrt{3^{2}}\sqrt{12^{4}}$$

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}.

$$a=1331\times 2\sqrt{2}\sqrt{3^{2}}\sqrt{12^{4}}$$

Multiply 1331 and 2 to get 2662.

$$a=2662\sqrt{2}\sqrt{3^{2}}\sqrt{12^{4}}$$

Calculate 3 to the power of 2 and get 9.

$$a=2662\sqrt{2}\sqrt{9}\sqrt{12^{4}}$$

Calculate the square root of 9 and get 3.

$$a=2662\sqrt{2}\times 3\sqrt{12^{4}}$$

Multiply 2662 and 3 to get 7986.

$$a=7986\sqrt{2}\sqrt{12^{4}}$$

Calculate 12 to the power of 4 and get 20736.

$$a=7986\sqrt{2}\sqrt{20736}$$

Calculate the square root of 20736 and get 144.

$$a=7986\sqrt{2}\times 144$$

Multiply 7986 and 144 to get 1149984.

$$a=1149984\sqrt{2}$$

Consider the second equation. Insert the known values of variables into the equation.

$$b=1149984\sqrt{2}$$

Consider the third equation. Insert the known values of variables into the equation.

$$c=1149984\sqrt{2}$$

The system is now solved.

$$a=1149984\sqrt{2} b=1149984\sqrt{2} c=1149984\sqrt{2}$$