Evaluate square root of 180

Problem

√(,180)

Solution

1. Identify the largest perfect square factor of the number inside the radical.

2. Factor the number 180 into a product of a perfect square and another integer.

180=36×5

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

√(,180)=√(,36×5)

√(,180)=√(,36)×√(,5)

4. Simplify the square root of the perfect square.

√(,36)=6

5. Combine the terms to reach the final simplified radical form.

6×√(,5)=6√(,5)

Final Answer

√(,180)=6√(,5)

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