Evaluate 6 square root of 19^3

Problem

6√(,19^3)

Solution

1. Rewrite the expression using the property of exponents for square roots, where √(,a^n)=a^n/2

6√(,19^3)=6⋅19^3/2

2. Decompose the power inside the square root to separate the perfect square.

6√(,19^3)=6√(,19^2⋅19)

3. Simplify the square root by taking the square root of 19^2

6√(,19^2⋅19)=6⋅19√(,19)

4. Multiply the coefficients 6 and 19

6⋅19=114

Final Answer

6√(,19^3)=114√(,19)

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