Calculate the square root of 180

Problem

√(,180)

Solution

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

2. Factor the number 180 into its prime components.

180=2⋅90

180=2⋅2⋅45

180=2⋅2⋅3⋅15

180=2⋅2⋅3⋅3⋅5

3. Group the factors into perfect squares.

180=2⋅3⋅5

4. Apply the property of radicals √(,a⋅b)=√(,a)⋅√(,b) to separate the perfect squares.

√(,180)=√(,2⋅3⋅5)

√(,180)=√(,2)⋅√(,3)⋅√(,5)

5. Simplify the square roots of the perfect squares.

√(,180)=2⋅3⋅√(,5)

√(,180)=6√(,5)

Final Answer

√(,180)=6√(,5)

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