Simplify square root of 40

Problem

√(,40)

Solution

1. Identify the largest perfect square factor of the radicand 40.

2. Factor the number 40 into the product of its largest perfect square factor and another integer.

40=4⋅10

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

√(,40)=√(,4⋅10)

√(,40)=√(,4)⋅√(,10)

4. Simplify the square root of the perfect square.

√(,4)=2

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

2⋅√(,10)=2√(,10)

Final Answer

√(,40)=2√(,10)

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