Solve sqrt{290/1400}=8/x

$$\sqrt { \frac { 290 } { 1400 } } = \frac { 8 } { x }$$

Solve for x

$$x = \frac{16 \sqrt{1015}}{29} \approx 17.577414976$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x\sqrt{\frac{290}{1400}}=8$$

Reduce the fraction \frac{290}{1400} to lowest terms by extracting and canceling out 10.

$$x\sqrt{\frac{29}{140}}=8$$

Rewrite the square root of the division \sqrt{\frac{29}{140}} as the division of square roots \frac{\sqrt{29}}{\sqrt{140}}.

$$x\times \frac{\sqrt{29}}{\sqrt{140}}=8$$

Factor 140=2^{2}\times 35. Rewrite the square root of the product \sqrt{2^{2}\times 35} as the product of square roots \sqrt{2^{2}}\sqrt{35}. Take the square root of 2^{2}.

$$x\times \frac{\sqrt{29}}{2\sqrt{35}}=8$$

Rationalize the denominator of \frac{\sqrt{29}}{2\sqrt{35}} by multiplying numerator and denominator by \sqrt{35}.

$$x\times \frac{\sqrt{29}\sqrt{35}}{2\left(\sqrt{35}\right)^{2}}=8$$

The square of \sqrt{35} is 35.

$$x\times \frac{\sqrt{29}\sqrt{35}}{2\times 35}=8$$

To multiply \sqrt{29} and \sqrt{35}, multiply the numbers under the square root.

$$x\times \frac{\sqrt{1015}}{2\times 35}=8$$

Multiply 2 and 35 to get 70.

$$x\times \frac{\sqrt{1015}}{70}=8$$

Express x\times \frac{\sqrt{1015}}{70} as a single fraction.

$$\frac{x\sqrt{1015}}{70}=8$$

Multiply both sides by 70.

$$x\sqrt{1015}=8\times 70$$

Multiply 8 and 70 to get 560.

$$x\sqrt{1015}=560$$

The equation is in standard form.

$$\sqrt{1015}x=560$$

Divide both sides by \sqrt{1015}.

$$\frac{\sqrt{1015}x}{\sqrt{1015}}=\frac{560}{\sqrt{1015}}$$

Dividing by \sqrt{1015} undoes the multiplication by \sqrt{1015}.

$$x=\frac{560}{\sqrt{1015}}$$

Divide 560 by \sqrt{1015}.

$$x=\frac{16\sqrt{1015}}{29}$$