Evaluate square root of 8+ square root of 18

Problem

√(,8)+√(,18)

Solution

1. Identify the radicals that can be simplified by finding the largest perfect square factors of the radicands.

2. Factor the number 8 into 4×2 and the number 18 into 9×2

3. Apply the product property of radicals, √(,a×b)=√(,a)×√(,b) to separate the perfect squares.

√(,8)=√(,4×2)=√(,4)×√(,2)=2√(,2)

√(,18)=√(,9×2)=√(,9)×√(,2)=3√(,2)

4. Substitute the simplified forms back into the original expression.

2√(,2)+3√(,2)

5. Combine the like terms by adding the coefficients.

(2+3)√(,2)=5√(,2)

Final Answer

√(,8)+√(,18)=5√(,2)

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