Calculate the square root of 112

Problem

√(,112)

Solution

1. Identify the number inside the radical and look for its prime factors.

2. Factor the number 112 into its prime components.

112=2×56

112=2×2×28

112=2×2×2×14

112=2×2×2×2×7

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

112=2×7

112=16×7

4. Apply the product property of square roots, which states √(,a×b)=√(,a)×√(,b)

√(,112)=√(,16×7)

5. Simplify the square root of the perfect square.

√(,16)×√(,7)=4√(,7)

Final Answer

√(,112)=4√(,7)

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