Simplify square root of 384x^4y^3

Problem

√(,384*x4*y3)

Solution

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

384=64⋅6

2. Rewrite the variables x4 and y3 as products of perfect squares.

x4=(x2)2

y3=y2⋅y

3. Group all perfect square terms under the radical.

√(,64⋅6⋅(x2)2⋅y2⋅y)

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

√(,64)⋅√(,(x2)2)⋅√(,y2)⋅√(,6*y)

5. Simplify the square roots of the perfect squares.

8⋅x2⋅y⋅√(,6*y)

Final Answer

√(,384*x4*y3)=8*x2*y√(,6*y)

Want more problems? Check here!