Question 396535
{{{27X^2/25 = 1/3}}}
First let's eliminate the fraction by multiplying both sides by 25:
{{{27X^2 = 25/3}}}
Dividing both sides by 27 isolates the base, x, and its exponent, 2:
{{{X^2 = 25/81}}}
Now we can find the square root of each side:
{{{sqrt(X^2) = sqrt(25/81)}}}
On the left side we get not "x" but {{{abs(x)}}}. This is so because a square root is supposed to be positive but we do not know if x is positive. Using absolute value like this ensures that we get a positive square root.
{{{abs(X) = sqrt(25/81)}}}
On the right side we can use a property of radicals, {{{root(a, p)/root(a, q) = root(a, p/q)}}}, to split the square root of a fraction into a fraction of the square roots of the numerator and denominator:
{{{abs(X) = sqrt(25)/sqrt(81)}}}
which simplifies to:
{{{abs(x) = 5/9}}}
Solving the absolute value equation we get:
{{{x = 5/9}}} or {{{x = (-5)/9}}}
These are both solutions to your equation.