Simplify ( square root of 3)/( square root of 22)

Problem

√(,3)/√(,22)

Solution

1. Identify the expression as a fraction involving square roots in both the numerator and the denominator.

2. Rationalize the denominator by multiplying both the numerator and the denominator by √(,22) to remove the radical from the bottom.

3. Multiply the terms in the numerator using the property √(,a)⋅√(,b)=√(,a*b)

√(,3)⋅√(,22)=√(,66)

4. Multiply the terms in the denominator.

√(,22)⋅√(,22)=22

5. Check for simplification of the radical √(,66) Since the prime factorization of 66 is 2⋅3⋅11 there are no perfect square factors, so the radical cannot be simplified further.

Final Answer

√(,3)/√(,22)=√(,66)/22

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