Solve sqrt{27/30}=x/60

$$\sqrt { \frac { 27 } { 30 } } = \frac { x } { 60 }$$

Solve for x

$$x=18\sqrt{10}\approx 56.920997883$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60.

$$60\sqrt{\frac{27}{30}}=x$$

Reduce the fraction \frac{27}{30} to lowest terms by extracting and canceling out 3.

$$60\sqrt{\frac{9}{10}}=x$$

Rewrite the square root of the division \sqrt{\frac{9}{10}} as the division of square roots \frac{\sqrt{9}}{\sqrt{10}}.

$$60\times \frac{\sqrt{9}}{\sqrt{10}}=x$$

Calculate the square root of 9 and get 3.

$$60\times \frac{3}{\sqrt{10}}=x$$

Rationalize the denominator of \frac{3}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$60\times \frac{3\sqrt{10}}{\left(\sqrt{10}\right)^{2}}=x$$

The square of \sqrt{10} is 10.

$$60\times \frac{3\sqrt{10}}{10}=x$$

Cancel out 10, the greatest common factor in 60 and 10.

$$6\times 3\sqrt{10}=x$$

Multiply 6 and 3 to get 18.

$$18\sqrt{10}=x$$

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

$$x=18\sqrt{10}$$