Simplify square root of 150

Problem

√(,150)

Solution

1. Identify the largest perfect square factor of the radicand 150.

2. Factor 150 into the product of a perfect square and another integer.

√(,150)=√(,25⋅6)

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

√(,25⋅6)=√(,25)⋅√(,6)

4. Simplify the square root of the perfect square.

√(,25)⋅√(,6)=5√(,6)

Final Answer

√(,150)=5√(,6)

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