Simplify fourth root of 243

Problem

√(4,243)

Solution

1. Find the prime factorization of the number under the radical.

243=3⋅81

243=3⋅3⋅27

243=3⋅3⋅3⋅9

243=3⋅3⋅3⋅3⋅3

243=3

2. Rewrite the expression using the prime factorization.

√(4,3)

3. Apply the property of radicals √(n,am)=am/n or split the power into a multiple of the index.

√(4,3⋅3)

4. Simplify the radical by taking the fourth root of the perfect fourth power.

√(4,3)⋅√(4,3)

3⋅√(4,3)

Final Answer

√(4,243)=3√(4,3)

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