Evaluate square root of 150

Problem

√(,150)

Solution

1. Identify the radicand and look for perfect square factors.

2. Factor the number 150 into a product of its prime factors or a product involving the largest perfect square.

150=25⋅6

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

√(,150)=√(,25⋅6)

√(,150)=√(,25)⋅√(,6)

4. Simplify the square root of the perfect square.

√(,25)=5

5. Combine the terms to reach the simplest radical form.

5⋅√(,6)=5√(,6)

Final Answer

√(,150)=5√(,6)

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