Solve x*sqrt{4*5/7}=53

$$x \times \sqrt{ 4 \times \frac { 5 } { 7 } } =53$$

Solve for x

$$x = \frac{53 \sqrt{35}}{10} \approx 31.35522285$$

Steps for Solving Linear Equation

Express 4\times \frac{5}{7} as a single fraction.

$$x\sqrt{\frac{4\times 5}{7}}=53$$

Multiply 4 and 5 to get 20.

$$x\sqrt{\frac{20}{7}}=53$$

Rewrite the square root of the division \sqrt{\frac{20}{7}} as the division of square roots \frac{\sqrt{20}}{\sqrt{7}}.

$$x\times \frac{\sqrt{20}}{\sqrt{7}}=53$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$x\times \frac{2\sqrt{5}}{\sqrt{7}}=53$$

Rationalize the denominator of \frac{2\sqrt{5}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$x\times \frac{2\sqrt{5}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}=53$$

The square of \sqrt{7} is 7.

$$x\times \frac{2\sqrt{5}\sqrt{7}}{7}=53$$

To multiply \sqrt{5} and \sqrt{7}, multiply the numbers under the square root.

$$x\times \frac{2\sqrt{35}}{7}=53$$

Express x\times \frac{2\sqrt{35}}{7} as a single fraction.

$$\frac{x\times 2\sqrt{35}}{7}=53$$

Multiply both sides by 7.

$$x\times 2\sqrt{35}=53\times 7$$

Multiply 53 and 7 to get 371.

$$x\times 2\sqrt{35}=371$$

The equation is in standard form.

$$2\sqrt{35}x=371$$

Divide both sides by 2\sqrt{35}.

$$\frac{2\sqrt{35}x}{2\sqrt{35}}=\frac{371}{2\sqrt{35}}$$

Dividing by 2\sqrt{35} undoes the multiplication by 2\sqrt{35}.

$$x=\frac{371}{2\sqrt{35}}$$

Divide 371 by 2\sqrt{35}.

$$x=\frac{53\sqrt{35}}{10}$$