Evaluate square root of 666

Problem

√(,666)

Solution

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

2. Factor the number 666 into its prime factors or find the largest perfect square that divides it.

666=2⋅333

666=2⋅9⋅37

3. Rewrite the square root using the factors found, specifically identifying the perfect square 9

√(,666)=√(,9⋅74)

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

√(,666)=√(,9)⋅√(,74)

5. Simplify the square root of the perfect square.

√(,9)=3

6. Combine the results to get the simplified radical form.

√(,666)=3√(,74)

Final Answer

√(,666)=3√(,74)

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