Solve sqrt{1+55/729}=1+x/27

$$\sqrt{ 1+ \frac{ 55 }{ 729 } } =1+ \frac{ x }{ 27 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 27.

$$27\sqrt{1+\frac{55}{729}}=27+x$$

Convert 1 to fraction \frac{729}{729}.

$$27\sqrt{\frac{729}{729}+\frac{55}{729}}=27+x$$

Since \frac{729}{729} and \frac{55}{729} have the same denominator, add them by adding their numerators.

$$27\sqrt{\frac{729+55}{729}}=27+x$$

Add 729 and 55 to get 784.

$$27\sqrt{\frac{784}{729}}=27+x$$

Rewrite the square root of the division \frac{784}{729} as the division of square roots \frac{\sqrt{784}}{\sqrt{729}}. Take the square root of both numerator and denominator.

$$27\times \frac{28}{27}=27+x$$

Cancel out 27 and 27.

$$28=27+x$$

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

$$27+x=28$$

Subtract 27 from both sides.

$$x=28-27$$

Subtract 27 from 28 to get 1.

$$x=1$$