Final answer:
The expression √25y^2/6x simplifies to 5y√(6x)/6x, where 5 is the square root of 25 and y is the square root of y^2.
Step-by-step explanation:
To simplify the expression √25y^2/6x, we first consider the square root of each component separately. The square root of 25 is 5 because 5² equals 25, and the square root of y^2 is y because y multiplied by itself yields y^2. Therefore, √25y^2 simplifies to 5y. On simplifying √25y^2/6x, we get (5y)/√(6x), but since we generally do not leave square roots in the denominator, we rationalize the denominator by multiplying the numerator and the denominator by √(6x) giving us:
(5y√(6x))/(6x√(6x)) = (5y√(6x))/(6x) = 5y√(6x)/6x
Thus, the simplified form of the expression √25y^2/6x is 5y√(6x)/6x.