Simplify cube root of 64y^6

Problem

√(3,64*y^6)

Solution

1. Rewrite the expression using the property of radicals √(n,a*b)=√(n,a)⋅√(n,b) to separate the constant and the variable.

√(3,64)⋅√(3,y^6)

2. Evaluate the cube root of the constant by identifying that 4^3=64

√(3,64)=4

3. Apply the rule for radicals and exponents √(n,x^m)=x^(m/n) to simplify the variable term.

√(3,y^6)=y^(6/3)

4. Simplify the exponent by performing the division.

y^(6/3)=y^2

5. Combine the simplified parts to reach the final result.

4⋅y^2=4*y^2

Final Answer

√(3,64*y^6)=4*y^2

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