Simplify ( square root of 3)/( square root of 33)

Problem

√(,3)/√(,33)

Solution

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

√(,3)/√(,33)=√(,3/33)

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

√(,3/33)=√(,1/11)

3. Apply the quotient property in reverse to separate the square root of the numerator and the denominator.

√(,1/11)=√(,1)/√(,11)

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

√(,1)/√(,11)=1/√(,11)

5. Rationalize the denominator by multiplying both the numerator and the denominator by √(,11)

1/√(,11)⋅√(,11)/√(,11)=√(,11)/11

Final Answer

√(,3)/√(,33)=√(,11)/11

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