Simplify square root of 588

Problem

√(,588)

Solution

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

588=2×294

294=2×147

147=3×49

49=7×7

2. Group the prime factors into pairs of perfect squares.

588=2×7×3

3. Apply the property of radicals √(,a×b)=√(,a)×√(,b) to separate the perfect squares.

√(,588)=√(,2×7×3)

√(,588)=√(,2)×√(,7)×√(,3)

4. Simplify the square roots of the perfect squares.

√(,588)=2×7×√(,3)

√(,588)=14√(,3)

Final Answer

√(,588)=14√(,3)

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