Evaluate

Problem

(9√(,5)−5√(,6))*(3√(,5)+2√(,6))

Solution

1. Apply the FOIL method to multiply the two binomials by distributing each term in the first set of parentheses to each term in the second.

(9√(,5))*(3√(,5))+(9√(,5))*(2√(,6))−(5√(,6))*(3√(,5))−(5√(,6))*(2√(,6))

2. Multiply the coefficients and the radicals in each term, using the property √(,a)√(,b)=√(,a*b)

27√(,25)+18√(,30)−15√(,30)−10√(,36)

3. Simplify the square roots of the perfect squares, where √(,25)=5 and √(,36)=6

27*(5)+18√(,30)−15√(,30)−10*(6)

4. Calculate the products of the integers.

135+18√(,30)−15√(,30)−60

5. Combine like terms by subtracting the integers and combining the terms involving √(,30)

75+3√(,30)

Final Answer

(9√(,5)−5√(,6))*(3√(,5)+2√(,6))=75+3√(,30)

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