Evaluate square root of (1-3/5)/2

Problem

√(,(1−3/5)/2)

Solution

1. Simplify the numerator inside the square root by finding a common denominator for the subtraction.

5/5−3/5=2/5

2. Substitute the simplified numerator back into the main fraction.

2/5/2

3. Divide the fraction by 2, which is equivalent to multiplying the denominator by 2.

2/(5⋅2)=2/10

4. Reduce the fraction to its simplest form.

2/10=1/5

5. Apply the square root to the simplified fraction.

√(,1/5)

6. Rationalize the denominator by multiplying the numerator and denominator by √(,5)

1/√(,5)⋅√(,5)/√(,5)=√(,5)/5

Final Answer

√(,(1−3/5)/2)=√(,5)/5

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