Simplify square root of 384x^4y^3

Problem

√(,384*x^4*y^3)

Solution

1. Factor the constant 384 into its prime factors or identify the largest perfect square factor.

384=64⋅6

2. Rewrite the variables x^4 and y^3 as products of perfect squares.

x^4=(x^2)^2

y^3=y^2⋅y

3. Group all perfect square terms under the radical.

√(,64⋅6⋅(x^2)^2⋅y^2⋅y)

4. Apply the product rule for radicals √(,a⋅b)=√(,a)⋅√(,b) to separate the perfect squares.

√(,64)⋅√(,(x^2)^2)⋅√(,y^2)⋅√(,6*y)

5. Simplify the square roots of the perfect squares.

8⋅x^2⋅y⋅√(,6*y)

Final Answer

√(,384*x^4*y^3)=8*x^2*y√(,6*y)

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