Solve sqrt{4.5/1.7}=2pix

$$\sqrt { \frac { 4.5 } { 1.7 } } = 2 \pi x$$

Solve for x

$$x=\frac{3\sqrt{85}}{34\pi }\approx 0.25894166$$

Steps for Solving Linear Equation

Expand \frac{4.5}{1.7} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{45}{17}}=2\pi x$$

Rewrite the square root of the division \sqrt{\frac{45}{17}} as the division of square roots \frac{\sqrt{45}}{\sqrt{17}}.

$$\frac{\sqrt{45}}{\sqrt{17}}=2\pi x$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{3\sqrt{5}}{\sqrt{17}}=2\pi x$$

Rationalize the denominator of \frac{3\sqrt{5}}{\sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

$$\frac{3\sqrt{5}\sqrt{17}}{\left(\sqrt{17}\right)^{2}}=2\pi x$$

The square of \sqrt{17} is 17.

$$\frac{3\sqrt{5}\sqrt{17}}{17}=2\pi x$$

To multiply \sqrt{5} and \sqrt{17}, multiply the numbers under the square root.

$$\frac{3\sqrt{85}}{17}=2\pi x$$

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

$$2\pi x=\frac{3\sqrt{85}}{17}$$

Multiply both sides of the equation by 17.

$$34\pi x=3\sqrt{85}$$

Divide both sides by 34\pi .

$$\frac{34\pi x}{34\pi }=\frac{3\sqrt{85}}{34\pi }$$

Dividing by 34\pi undoes the multiplication by 34\pi .

$$x=\frac{3\sqrt{85}}{34\pi }$$