Evaluate square root of 12+ square root of 27

Problem

√(,12)+√(,27)

Solution

1. Simplify the first radical by factoring out the largest perfect square from the radicand.

√(,12)=√(,4⋅3)

√(,12)=2√(,3)

2. Simplify the second radical by factoring out the largest perfect square from the radicand.

√(,27)=√(,9⋅3)

√(,27)=3√(,3)

3. Combine the like terms by adding the coefficients of the common radical √(,3)

2√(,3)+3√(,3)=(2+3)√(,3)

2√(,3)+3√(,3)=5√(,3)

Final Answer

√(,12)+√(,27)=5√(,3)

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