Simplify square root of 50

Problem

√(,50)

Solution

1. Identify the radicand, which is 50 and look for its largest perfect square factor.

2. Factor the number 50 into a product of a perfect square and another number.

50=25⋅2

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

√(,50)=√(,25⋅2)

√(,50)=√(,25)⋅√(,2)

4. Simplify the square root of the perfect square 25

√(,25)=5

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

5⋅√(,2)=5√(,2)

Final Answer

√(,50)=5√(,2)

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