Simplify square root of 45

Problem

√(,45)

Solution

1. Identify the largest perfect square factor of the radicand 45.

2. Factor the number 45 into the product of that perfect square and another integer.

√(,45)=√(,9⋅5)

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

√(,9⋅5)=√(,9)⋅√(,5)

4. Evaluate the square root of the perfect square 9.

√(,9)⋅√(,5)=3√(,5)

Final Answer

√(,45)=3√(,5)

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