Simplify cube root of square root of 64x^6

Problem

√(3,√(,64*x6))

Solution

1. Rewrite the inner square root using an exponent.

√(,64*x6)=(64*x6)(1/2)

2. Simplify the inner expression by applying the power to each factor.

(64)(1/2)⋅(x6)(1/2)=8*x3

3. Substitute the simplified inner expression back into the cube root.

√(3,8*x3)

4. Rewrite the cube root as an exponent.

(8*x3)(1/3)

5. Apply the exponent to each factor to find the final result.

(8)(1/3)⋅(x3)(1/3)=2*x

Final Answer

√(3,√(,64*x6))=2*x

Want more problems? Check here!