Simplify ( square root of 2)/( square root of 34)

Problem

√(,2)/√(,34)

Solution

1. Combine the radicals using the quotient property of square roots, which states that √(,a)/√(,b)=√(,a/b)

√(,2)/√(,34)=√(,2/34)

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

√(,2/34)=√(,1/17)

3. Apply the quotient property in reverse to separate the radicals.

√(,1/17)=√(,1)/√(,17)

4. Evaluate the square root of the numerator.

√(,1)/√(,17)=1/√(,17)

5. Rationalize the denominator by multiplying both the numerator and the denominator by √(,17)

1/√(,17)⋅√(,17)/√(,17)=√(,17)/17

Final Answer

√(,2)/√(,34)=√(,17)/17

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