Evaluate square root of 250

Problem

√(,250)

Solution

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

250=2⋅125

250=2⋅5⋅25

250=2⋅5⋅5⋅5

2. Group the factors into perfect squares to simplify the radical.

250=25⋅10

250=5⋅10

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

√(,250)=√(,25⋅10)

√(,250)=√(,25)⋅√(,10)

4. Simplify the square root of the perfect square.

√(,25)=5

√(,250)=5√(,10)

Final Answer

√(,250)=5√(,10)

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