Calculate the square root of 72

Problem

√(,72)

Solution

1. Identify the number inside the radical and look for its largest perfect square factor.

2. Factor the number 72 into a product of a perfect square and another integer.

√(,72)=√(,36⋅2)

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

√(,36⋅2)=√(,36)⋅√(,2)

4. Simplify the square root of the perfect square.

√(,36)=6

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

6⋅√(,2)=6√(,2)

Final Answer

√(,72)=6√(,2)

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