Simplify square root of 9a^3+ square root of a

Problem

√(,9*a3)+√(,a)

Solution

1. Factor the first radical by identifying the perfect square components within the radicand 9*a3

√(,9⋅a2⋅a)+√(,a)

2. Apply the product rule for radicals, √(,x*y)=√(,x)√(,y) to separate the perfect squares from the remaining factor.

√(,9)⋅√(,a2)⋅√(,a)+√(,a)

3. Simplify the square roots of the perfect squares, noting that √(,9)=3 and √(,a2)=a (assuming a≥0.

3*a√(,a)+√(,a)

4. Combine like terms by factoring out the common radical factor √(,a)

(3*a+1)√(,a)

Final Answer

√(,9*a3)+√(,a)=(3*a+1)√(,a)

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