Simplify square root of 20x^16

Problem

√(,20*x^16)

Solution

1. Rewrite the radicand by factoring the constant into its prime factors or a product involving a perfect square.

√(,4⋅5⋅x^16)

2. Apply the product property of radicals, which states √(,a⋅b)=√(,a)⋅√(,b)

√(,4)⋅√(,5)⋅√(,x^16)

3. Evaluate the square root of the perfect square constant.

2⋅√(,5)⋅√(,x^16)

4. Simplify the variable expression by dividing the exponent by the index of the radical (which is 2).

2⋅√(,5)⋅x^8

5. Rearrange the terms to place the radical at the end of the expression.

2*x^8√(,5)

Final Answer

√(,20*x^16)=2*x^8√(,5)

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