Evaluate (25x)/( square root of 125x^3y)

Problem

(25*x)/√(,125*x^3*y)

Solution

1. Rewrite the expression using mathematical notation to clarify the radicand.

(25*x)/√(,125*x^3*y)

2. Factor the radicand into perfect squares and remaining factors to prepare for simplification.

√(,125*x^3*y)=√(,25⋅5⋅x^2⋅x⋅y)

3. Simplify the square root by taking the square root of the perfect square factors 25 and x^2

√(,125*x^3*y)=5*x√(,5*x*y)

4. Substitute the simplified radical back into the original fraction.

(25*x)/(5*x√(,5*x*y))

5. Cancel the common factors 5 and x from the numerator and the denominator.

5/√(,5*x*y)

6. Rationalize the denominator by multiplying both the numerator and the denominator by √(,5*x*y)

(5√(,5*x*y))/(√(,5*x*y)√(,5*x*y))

7. Simplify the denominator and cancel the common factor 5

(5√(,5*x*y))/(5*x*y)

√(,5*x*y)/(x*y)

Final Answer

(25*x)/√(,125*x^3*y)=√(,5*x*y)/(x*y)

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