Simplify square root of 112

Problem

√(,112)

Solution

1. Identify the prime factors of the number inside the radical.

112=2×56

112=2×2×28

112=2×2×2×14

112=2×2×2×2×7

2. Group the factors into pairs of perfect squares.

112=2×7

112=16×7

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

√(,112)=√(,16×7)

√(,112)=√(,16)×√(,7)

4. Simplify the square root of the perfect square.

√(,16)=4

√(,112)=4√(,7)

Final Answer

√(,112)=4√(,7)

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