Evaluate 4 square root of 200

Problem

4√(,200)

Solution

1. Identify the radicand and look for the largest perfect square factor within it.

2. Factor the number 200 into 100×2 where 100 is a perfect square.

4√(,100×2)

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

4×√(,100)×√(,2)

4. Evaluate the square root of the perfect square 100

4×10×√(,2)

5. Multiply the coefficients outside the radical.

40√(,2)

Final Answer

4√(,200)=40√(,2)

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