Calculate the square root of 288

Problem

√(,288)

Solution

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

2. Factor the number 288 into a product of its prime factors or a product involving the largest possible perfect square.

288=144⋅2

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

√(,288)=√(,144⋅2)

√(,288)=√(,144)⋅√(,2)

4. Simplify the square root of the perfect square 144

√(,144)=12

5. Combine the results to find the simplified radical form.

√(,288)=12√(,2)

Final Answer

√(,288)=12√(,2)

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