simplify the expression sqrt(5/3)
To simplify the expression sqrt(5/3), we need to find the square root of the fraction 5/3.
To do this, we can simplify the fraction first.
The square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator.
So, in this case, we have:
sqrt(5/3) = sqrt(5) / sqrt(3)
However, we usually prefer to rationalize the denominator, which means eliminating any radicals from the denominator.
To rationalize the denominator of sqrt(5/3), we can multiply both the numerator and denominator by the square root of 3.
sqrt(5/3) * sqrt(3)/sqrt(3) = (sqrt(5) * sqrt(3)) / sqrt(3) * sqrt(3)
Simplifying further:
= sqrt(5*3) / sqrt(3*3)
= sqrt(15) / 3
So, the simplified expression of sqrt(5/3) is sqrt(15)/3.