Simplify square root of 180

Problem

√(,180)

Solution

1. Find the prime factorization of the number inside the radical to identify perfect square factors.

180=2⋅90=2⋅2⋅45=2⋅3⋅5

2. Group the factors into the largest possible perfect square and the remaining non-square part.

180=36⋅5

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

√(,180)=√(,36⋅5)

4. Simplify the square root of the perfect square.

√(,36⋅5)=√(,36)⋅√(,5)

5. Calculate the final value by taking the square root of 36.

6⋅√(,5)

Final Answer

√(,180)=6√(,5)

Want more problems? Check here!