Simplify cube root of 64y^6

Problem

√(3,64*y6)

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,y6)

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

√(3,64)=4

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

√(3,y6)=y(6/3)

4. Simplify the exponent by performing the division.

y(6/3)=y2

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

4⋅y2=4*y2

Final Answer

√(3,64*y6)=4*y2

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