Simplify square root of 243

Problem

√(,243)

Solution

1. Identify the prime factorization of the number inside the square root.

243=3×81

243=3×3×27

243=3×3×3×9

243=3×3×3×3×3

243=3

2. Rewrite the expression by grouping the factors into perfect squares.

√(,243)=√(,3×3)

√(,243)=√(,81×3)

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

√(,243)=√(,81)×√(,3)

4. Simplify the square root of the perfect square.

√(,81)=9

√(,243)=9√(,3)

Final Answer

√(,243)=9√(,3)

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