Evaluate square root of 164

Problem

√(,164)

Solution

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

2. Factor the number 164 into its prime factors or find the largest perfect square that divides it.

164=4×41

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

√(,164)=√(,4×41)

√(,164)=√(,4)×√(,41)

4. Simplify the square root of the perfect square factor.

√(,4)=2

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

√(,164)=2√(,41)

Final Answer

√(,164)=2√(,41)

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