Simplify square root of 25x^6

Problem

√(,25*x6)

Solution

1. Apply the product property of radicals to separate the constant and the variable parts.

√(,25⋅x6)=√(,25)⋅√(,x6)

2. Evaluate the square root of the constant coefficient 25

√(,25)=5

3. Simplify the radical of the variable part by dividing the exponent by the index of the root, which is 2

√(,x6)=x(6/2)

4. Perform the division in the exponent to find the final power of x

x(6/2)=x3

5. Combine the results to obtain the simplified expression.

5⋅x3=5*x3

Final Answer

√(,25*x6)=5*x3

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