Solve AB=sqrt{32}-3sqrt{2}+sqrt{18}

$$A B = \sqrt { 32 } - 3 \sqrt { 2 } + \sqrt { 18 }$$

Solve for A

$$A=\frac{4\sqrt{2}}{B}$$

$$B\neq 0$$

Steps for Solving Linear Equation

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}.

$$AB=4\sqrt{2}-3\sqrt{2}+\sqrt{18}$$

Combine 4\sqrt{2} and -3\sqrt{2} to get \sqrt{2}.

$$AB=\sqrt{2}+\sqrt{18}$$

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}.

$$AB=\sqrt{2}+3\sqrt{2}$$

Combine \sqrt{2} and 3\sqrt{2} to get 4\sqrt{2}.

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

The equation is in standard form.

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

Divide both sides by B.

$$\frac{BA}{B}=\frac{4\sqrt{2}}{B}$$

Dividing by B undoes the multiplication by B.

$$A=\frac{4\sqrt{2}}{B}$$

Solve for B

$$B=\frac{4\sqrt{2}}{A}$$

$$A\neq 0$$

Steps for Solving Linear Equation

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}.

$$AB=4\sqrt{2}-3\sqrt{2}+\sqrt{18}$$

Combine 4\sqrt{2} and -3\sqrt{2} to get \sqrt{2}.

$$AB=\sqrt{2}+\sqrt{18}$$

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}.

$$AB=\sqrt{2}+3\sqrt{2}$$

Combine \sqrt{2} and 3\sqrt{2} to get 4\sqrt{2}.

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

Divide both sides by A.

$$\frac{AB}{A}=\frac{4\sqrt{2}}{A}$$

Dividing by A undoes the multiplication by A.

$$B=\frac{4\sqrt{2}}{A}$$