Evaluate square root of 162

Problem

√(,162)

Solution

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

2. Factor the number 162 into a product of a perfect square and another integer.

162=81⋅2

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

√(,81⋅2)=√(,81)⋅√(,2)

4. Simplify the square root of the perfect square 81

√(,81)=9

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

9⋅√(,2)=9√(,2)

Final Answer

√(,162)=9√(,2)

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