Evaluate square root of 40

Problem

√(,40)

Solution

1. Identify the number under the radical and look for its perfect square factors.

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

√(,40)=√(,4⋅10)

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

√(,4⋅10)=√(,4)⋅√(,10)

4. Simplify the square root of the perfect square.

√(,4)=2

5. Combine the results to write the expression in simplest radical form.

2⋅√(,10)=2√(,10)

Final Answer

√(,40)=2√(,10)

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