Simplify cube root of 54a^7b^4

Problem

√(3,54*a^7*b^4)

Solution

1. Factor the constant 54 into its prime factors to identify perfect cubes.

54=2⋅27=2⋅3^3

2. Rewrite the variables a^7 and b^4 using the largest exponents that are multiples of the index 3

a^7=a^6⋅a^1

b^4=b^3⋅b^1

3. Group all perfect cubes together inside the radical.

√(3,3^3⋅a^6⋅b^3⋅2⋅a⋅b)

4. Extract the perfect cubes from the radical by dividing their exponents by 3

√(3,3^3)=3

√(3,a^6)=a^2

√(3,b^3)=b

5. Simplify the expression by placing the extracted terms outside the radical and leaving the remaining factors inside.

3*a^2*b√(3,2*a*b)

Final Answer

√(3,54*a^7*b^4)=3*a^2*b√(3,2*a*b)

Want more problems? Check here!