Simplify (( square root of 2)/2)^2

Problem

(√(,2)/2)2

Solution

1. Apply the power of a quotient rule by squaring both the numerator and the denominator separately.

(√(,2)/2)2=((√(,2))2)/2

2. Simplify the numerator by recognizing that squaring a square root returns the original radicand.

(√(,2))2=2

3. Simplify the denominator by calculating the square of 2.

2=4

4. Combine the results into a single fraction.

2/4

5. Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

2/4=1/2

Final Answer

(√(,2)/2)2=1/2

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