Simplify square root of 200

Problem

√(,200)

Solution

1. Identify the largest perfect square factor of the radicand 200

2. Factor the number 200 into the product of a perfect square and another integer.

√(,200)=√(,100⋅2)

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

√(,100⋅2)=√(,100)⋅√(,2)

4. Evaluate the square root of the perfect square 100

√(,100)=10

5. Combine the results to write the expression in simplest radical form.

10⋅√(,2)=10√(,2)

Final Answer

√(,200)=10√(,2)

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