Simplify ( square root of 3)/( square root of 6)

Problem

√(,3)/√(,6)

Solution

1. Apply the quotient property of square roots to combine the numerator and denominator into a single radical.

√(,3)/√(,6)=√(,3/6)

2. Simplify the fraction inside the square root by dividing both the numerator and the denominator by their greatest common factor, 3.

√(,3/6)=√(,1/2)

3. Distribute the square root back to the numerator and the denominator.

√(,1/2)=√(,1)/√(,2)

4. Evaluate the square root of 1 in the numerator.

√(,1)/√(,2)=1/√(,2)

5. Rationalize the denominator by multiplying both the numerator and the denominator by √(,2)

1/√(,2)⋅√(,2)/√(,2)=√(,2)/2

Final Answer

√(,3)/√(,6)=√(,2)/2

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