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 1 and 3/5

5/5+3/5=8/5

2. Substitute the simplified numerator back into the expression.

√(,8/5/2)

3. Divide the fraction by 2 by multiplying the denominator of the fraction by 2

8/5÷2=8/10

4. Reduce the fraction 8/10 to its simplest form.

8/10=4/5

5. Apply the square root to the simplified fraction.

√(,4/5)=√(,4)/√(,5)

6. Evaluate the square root of the numerator.

2/√(,5)

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

(2⋅√(,5))/(√(,5)⋅√(,5))=(2√(,5))/5

Final Answer

√(,(1+3/5)/2)=(2√(,5))/5

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