Simplify square root of square root of 81x^4

Problem

√(,√(,81*x^4))

Solution

1. Apply the property of nested radicals to combine the square roots into a single root by multiplying the indices.

√(,√(,81*x^4))=√(4,81*x^4)

2. Rewrite the radicand as a single expression raised to the fourth power.

81*x^4=3^4*x^4

3. Apply the power of a product rule to group the terms under the same exponent.

3^4*x^4=(3*x)^4

4. Simplify the fourth root of the fourth power, assuming x≥0

√(4,(3*x)^4)=3*x

Final Answer

√(,√(,81*x^4))=3*x

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