Solve sqrt{8}+3=m*sqrt{2}

$$\sqrt { 8 } + 3 = m \cdot \sqrt { 2 }$$

Solve for m

$$m=\frac{3\sqrt{2}}{2}+2\approx 4.121320344$$

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}.

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

Swap sides so that all variable terms are on the left hand side.

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

The equation is in standard form.

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

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}m}{\sqrt{2}}=\frac{2\sqrt{2}+3}{\sqrt{2}}$$

Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.

$$m=\frac{2\sqrt{2}+3}{\sqrt{2}}$$

Divide 2\sqrt{2}+3 by \sqrt{2}.

$$m=\frac{3\sqrt{2}}{2}+2$$